三角関数厳密値の表

近似値では満足できない方、座標ゴリ押しを最終奥義とする方向けです。
複素数なしの四則根号のみで表されているで、計算自体はしやすい形になっていると思います。
使い道は限られますが、いざという時に参照できるものとして残しておきます。
$$ \begin{array}{|c|c||c|c|c|c|c|c|c|c|} \hline \theta & 度 & \sin\theta & \cos\theta & \tan\theta & \sec\theta & \csc\theta & \cot\theta & \mathrm{hav}\,\theta & \mathrm{sinc}\,\theta \\ \hline \hline 0 & 0 & 0 & 1 & 0 & 1 & 未定義 & 未定義 & 0 & 未定義 \\ \hline \frac{\pi }{60} & 3 & \frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{2 \sqrt{3} \left(\sqrt{5}-1\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}-1 & \frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{32} \left(16+\sqrt{2} \left(\sqrt{3}-\sqrt{15}-\sqrt{2 \left(5+\sqrt{5}\right)}\right)+\sqrt{2} \left(-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)\right) & \frac{15 \left(-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{2 \sqrt{2} \pi } \\ \hline \frac{\pi }{30} & 6 & \frac{1}{8} \left(-1-\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right) & -\frac{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{8}{\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & -\frac{8}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & -\frac{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(8-\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)\right) & -\frac{15 \left(1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}\right)}{4 \pi } \\ \hline \frac{\pi }{20} & 9 & \frac{1}{8} \left(\sqrt{2} \left(1+\sqrt{5}\right)-2 \sqrt{5-\sqrt{5}}\right) & \frac{1}{8} \left(2 \sqrt{5-\sqrt{5}}+\sqrt{2} \left(1+\sqrt{5}\right)\right) & 1-\frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}} & \frac{8}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}} & \frac{8}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & 1+\frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & \frac{1}{16} \left(8-2 \sqrt{5-\sqrt{5}}-\sqrt{2} \left(1+\sqrt{5}\right)\right) & \frac{5 \left(\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}\right)}{2 \pi } \\ \hline \frac{\pi }{16} & 11.25 & \frac{1}{2} \sqrt{2-\sqrt{2+\sqrt{2}}} & \frac{1}{2} \sqrt{2+\sqrt{2+\sqrt{2}}} & \sqrt{\frac{2-\sqrt{2+\sqrt{2}}}{2+\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}} & \sqrt{\frac{2+\sqrt{2+\sqrt{2}}}{2-\sqrt{2+\sqrt{2}}}} & \frac{1}{4} \left(2-\sqrt{2+\sqrt{2+\sqrt{2}}}\right) & \frac{8 \sqrt{2-\sqrt{2+\sqrt{2}}}}{\pi } \\ \hline \frac{\pi }{15} & 12 & \frac{1}{8} \left(\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}} & -\frac{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(9-\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{8 \pi } \\ \hline \frac{\pi }{12} & 15 & \frac{\sqrt{3}-1}{2 \sqrt{2}} & \frac{1+\sqrt{3}}{2 \sqrt{2}} & 2-\sqrt{3} & \sqrt{2} \left(\sqrt{3}-1\right) & \sqrt{2} \left(1+\sqrt{3}\right) & 2+\sqrt{3} & \frac{1}{8} \left(4-\sqrt{2} \left(1+\sqrt{3}\right)\right) & \frac{3 \sqrt{2} \left(\sqrt{3}-1\right)}{\pi } \\ \hline \frac{\pi }{10} & 18 & \frac{1}{4} \left(\sqrt{5}-1\right) & \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} & \sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}} & 1+\sqrt{5} & \sqrt{5+2 \sqrt{5}} & \frac{1}{2} \left(1-\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}\right) & \frac{5 \left(\sqrt{5}-1\right)}{2 \pi } \\ \hline \frac{7 \pi }{60} & 21 & \frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & 1+\frac{2 \sqrt{2 \left(5-\sqrt{5}\right)}-2 \sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & 1+\frac{2 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1}{32} \left(16-\sqrt{2}-\sqrt{10}+2 \sqrt{5-\sqrt{5}}-2 \sqrt{3 \left(5-\sqrt{5}\right)}-\sqrt{6} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)\right)}{14 \sqrt{2} \pi } \\ \hline \frac{\pi }{8} & 22.5 & \frac{\sqrt{2-\sqrt{2}}}{2} & \frac{\sqrt{2+\sqrt{2}}}{2} & \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}} & \frac{2}{\sqrt{2+\sqrt{2}}} & \frac{2}{\sqrt{2-\sqrt{2}}} & \sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}} & \frac{1}{4} \left(2-\sqrt{2+\sqrt{2}}\right) & \frac{4 \sqrt{2-\sqrt{2}}}{\pi } \\ \hline \frac{2 \pi }{15} & 24 & \frac{1}{8} \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right) & \frac{1}{8} \left(1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{\sqrt{3}+\sqrt{15}-\sqrt{2 \left(5-\sqrt{5}\right)}}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{8}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}-\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(7-\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{16 \pi } \\ \hline \frac{3 \pi }{20} & 27 & \frac{1}{8} \left(2 \sqrt{5+\sqrt{5}}-\sqrt{2} \left(\sqrt{5}-1\right)\right) & \frac{1}{8} \left(\sqrt{2} \left(\sqrt{5}-1\right)+2 \sqrt{5+\sqrt{5}}\right) & \frac{4 \sqrt{5+\sqrt{5}}}{-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}}-1 & \frac{8}{-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}} & \frac{8}{2 \sqrt{5+\sqrt{5}}-\sqrt{2} \left(\sqrt{5}-1\right)} & \frac{4 \sqrt{5+\sqrt{5}}}{\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}}-1 & \frac{1}{16} \left(8+\sqrt{2}-\sqrt{10}-2 \sqrt{5+\sqrt{5}}\right) & \frac{5 \left(\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}\right)}{6 \pi } \\ \hline \frac{\pi }{6} & 30 & \frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{1}{\sqrt{3}} & \frac{2}{\sqrt{3}} & 2 & \sqrt{3} & \frac{1}{4} \left(2-\sqrt{3}\right) & \frac{3}{\pi } \\ \hline \frac{11 \pi }{60} & 33 & \frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & 1+\frac{2 \left(\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & -\frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{32} \left(16+\sqrt{2}-\sqrt{10}+\sqrt{6} \left(\sqrt{5}-1\right)-2 \sqrt{5+\sqrt{5}}-2 \sqrt{3 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{22 \sqrt{2} \pi } \\ \hline \frac{3 \pi }{16} & 33.75 & \frac{1}{2} \left(\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right) & \frac{1}{2} \left(\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}\right) & \frac{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}}{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{1}{4} \left(2+\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}\right) & \frac{8 \left(\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right)}{3 \pi } \\ \hline \frac{\pi }{5} & 36 & \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} & \frac{1}{4} \left(1+\sqrt{5}\right) & \sqrt{5-2 \sqrt{5}} & \sqrt{5}-1 & \frac{1}{\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}} & \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{8} \left(3-\sqrt{5}\right) & \frac{5 \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}}{\pi } \\ \hline \frac{13 \pi }{60} & 39 & \frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{2 \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}-1 & \frac{8 \sqrt{2}}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1}{32} \left(16+\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}-2 \sqrt{3 \left(5-\sqrt{5}\right)}-\sqrt{6} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{26 \sqrt{2} \pi } \\ \hline \frac{7 \pi }{30} & 42 & \frac{1}{8} \left(1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{\sqrt{3}-\sqrt{15}-\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(8+\sqrt{3}-\sqrt{15}-\sqrt{2 \left(5+\sqrt{5}\right)}\right) & -\frac{15 \left(-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{28 \pi } \\ \hline \frac{\pi }{4} & 45 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 1 & \sqrt{2} & \sqrt{2} & 1 & \frac{1}{4} \left(2-\sqrt{2}\right) & \frac{2 \sqrt{2}}{\pi } \\ \hline \frac{4 \pi }{15} & 48 & \frac{1}{8} \left(\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{\sqrt{3}-\sqrt{15}-\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(7+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{32 \pi } \\ \hline \frac{17 \pi }{60} & 51 & \frac{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{2 \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}-1 & \frac{1}{32} \left(16-\sqrt{2}-\sqrt{10}-2 \sqrt{5-\sqrt{5}}+2 \sqrt{3 \left(5-\sqrt{5}\right)}-\sqrt{6} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{34 \sqrt{2} \pi } \\ \hline \frac{3 \pi }{10} & 54 & \frac{1}{4} \left(1+\sqrt{5}\right) & \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} & \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}} & \sqrt{5}-1 & \sqrt{5-2 \sqrt{5}} & \frac{1}{2} \left(1-\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}\right) & \frac{5 \left(1+\sqrt{5}\right)}{6 \pi } \\ \hline \frac{5 \pi }{16} & 56.25 & \frac{1}{2} \left(\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}\right) & \frac{1}{2} \left(\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right) & \frac{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{2}{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}}{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{1}{4} \left(2-\sqrt{2-\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right) & \frac{8 \left(\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}\right)}{5 \pi } \\ \hline \frac{19 \pi }{60} & 57 & \frac{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & -\frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & 1+\frac{2 \left(\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{32} \left(16+\sqrt{2}-\sqrt{10}-\sqrt{6} \left(\sqrt{5}-1\right)+2 \sqrt{5+\sqrt{5}}-2 \sqrt{3 \left(5+\sqrt{5}\right)}\right) & -\frac{15 \left(1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{38 \sqrt{2} \pi } \\ \hline \frac{\pi }{3} & 60 & \frac{\sqrt{3}}{2} & \frac{1}{2} & \sqrt{3} & 2 & \frac{2}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{4} & \frac{3 \sqrt{3}}{2 \pi } \\ \hline \frac{7 \pi }{20} & 63 & \frac{1}{8} \left(\sqrt{2} \left(\sqrt{5}-1\right)+2 \sqrt{5+\sqrt{5}}\right) & \frac{1}{8} \left(2 \sqrt{5+\sqrt{5}}-\sqrt{2} \left(\sqrt{5}-1\right)\right) & \frac{4 \sqrt{5+\sqrt{5}}}{\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}}-1 & \frac{8}{2 \sqrt{5+\sqrt{5}}-\sqrt{2} \left(\sqrt{5}-1\right)} & \frac{8}{-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}} & \frac{4 \sqrt{5+\sqrt{5}}}{-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}}-1 & \frac{1}{16} \left(8-\sqrt{2}+\sqrt{10}-2 \sqrt{5+\sqrt{5}}\right) & \frac{5 \left(-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}\right)}{14 \pi } \\ \hline \frac{11 \pi }{30} & 66 & \frac{1}{8} \left(1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right) & \frac{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}-\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{8}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{\sqrt{3}+\sqrt{15}-\sqrt{2 \left(5-\sqrt{5}\right)}}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(2 \left(4+\sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)}\right)-\sqrt{3} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right)}{44 \pi } \\ \hline \frac{3 \pi }{8} & 67.5 & \frac{\sqrt{2+\sqrt{2}}}{2} & \frac{\sqrt{2-\sqrt{2}}}{2} & \sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}} & \frac{2}{\sqrt{2-\sqrt{2}}} & \frac{2}{\sqrt{2+\sqrt{2}}} & \sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}} & \frac{1}{4} \left(2-\sqrt{2-\sqrt{2}}\right) & \frac{4 \sqrt{2+\sqrt{2}}}{3 \pi } \\ \hline \frac{23 \pi }{60} & 69 & \frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & 1+\frac{2 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & 1+\frac{2 \sqrt{2 \left(5-\sqrt{5}\right)}-2 \sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1}{32} \left(16-\sqrt{2}+\sqrt{6}+\sqrt{10} \left(\sqrt{3}-1\right)-2 \sqrt{5-\sqrt{5}}-2 \sqrt{3 \left(5-\sqrt{5}\right)}\right) & \frac{15 \left(1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{46 \sqrt{2} \pi } \\ \hline \frac{2 \pi }{5} & 72 & \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} & \frac{1}{4} \left(\sqrt{5}-1\right) & \sqrt{5+2 \sqrt{5}} & 1+\sqrt{5} & \frac{1}{\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}} & \sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{8} \left(5-\sqrt{5}\right) & \frac{5 \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}}{2 \pi } \\ \hline \frac{5 \pi }{12} & 75 & \frac{1+\sqrt{3}}{2 \sqrt{2}} & \frac{\sqrt{3}-1}{2 \sqrt{2}} & 2+\sqrt{3} & \sqrt{2} \left(1+\sqrt{3}\right) & \sqrt{2} \left(\sqrt{3}-1\right) & 2-\sqrt{3} & \frac{1}{8} \left(4+\sqrt{2}-\sqrt{6}\right) & \frac{3 \sqrt{2} \left(1+\sqrt{3}\right)}{5 \pi } \\ \hline \frac{13 \pi }{30} & 78 & \frac{1}{8} \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & -\frac{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(8+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{52 \pi } \\ \hline \frac{7 \pi }{16} & 78.75 & \frac{1}{2} \sqrt{2+\sqrt{2+\sqrt{2}}} & \frac{1}{2} \sqrt{2-\sqrt{2+\sqrt{2}}} & \sqrt{\frac{2+\sqrt{2+\sqrt{2}}}{2-\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}} & \sqrt{\frac{2-\sqrt{2+\sqrt{2}}}{2+\sqrt{2+\sqrt{2}}}} & \frac{1}{4} \left(2-\sqrt{2-\sqrt{2+\sqrt{2}}}\right) & \frac{8 \sqrt{2+\sqrt{2+\sqrt{2}}}}{7 \pi } \\ \hline \frac{9 \pi }{20} & 81 & \frac{1}{8} \left(2 \sqrt{5-\sqrt{5}}+\sqrt{2} \left(1+\sqrt{5}\right)\right) & \frac{1}{8} \left(\sqrt{2} \left(1+\sqrt{5}\right)-2 \sqrt{5-\sqrt{5}}\right) & 1+\frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & \frac{8}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & \frac{8}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}} & 1-\frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}} & \frac{1}{16} \left(8+2 \sqrt{5-\sqrt{5}}-\sqrt{2} \left(1+\sqrt{5}\right)\right) & \frac{5 \left(\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}\right)}{18 \pi } \\ \hline \frac{7 \pi }{15} & 84 & \frac{1}{8} \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right) & \frac{1}{8} \left(-1-\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & -\frac{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & -\frac{8}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{8}{\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & -\frac{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(9+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{56 \pi } \\ \hline \frac{29 \pi }{60} & 87 & \frac{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{2 \sqrt{3} \left(\sqrt{5}-1\right)+2 \sqrt{2 \left(5+\sqrt{5}\right)}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}-1 & \frac{1}{32} \left(16+\sqrt{2}-\sqrt{10}-\sqrt{6} \left(\sqrt{5}-1\right)-2 \sqrt{5+\sqrt{5}}+2 \sqrt{3 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{58 \sqrt{2} \pi } \\ \hline \frac{\pi }{2} & 90 & 1 & 0 & 未定義 & 未定義 & 1 & 0 & \frac{1}{2} & \frac{2}{\pi } \\ \hline \frac{31 \pi }{60} & 93 & \frac{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & -\frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & 1+\frac{-2 \sqrt{3} \left(\sqrt{5}-1\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & -\frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & 1+\frac{-2 \sqrt{3} \left(\sqrt{5}-1\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{32} \left(16-\sqrt{2}+\sqrt{10}+\sqrt{6} \left(\sqrt{5}-1\right)+2 \sqrt{5+\sqrt{5}}-2 \sqrt{3 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{62 \sqrt{2} \pi } \\ \hline \frac{8 \pi }{15} & 96 & \frac{1}{8} \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right) & \frac{1}{8} \left(1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{8}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{8}{\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(7-\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{64 \pi } \\ \hline \frac{11 \pi }{20} & 99 & \frac{1}{8} \left(2 \sqrt{5-\sqrt{5}}+\sqrt{2} \left(1+\sqrt{5}\right)\right) & \frac{1}{8} \left(2 \sqrt{5-\sqrt{5}}-\sqrt{2} \left(1+\sqrt{5}\right)\right) & -1-\frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & -\frac{8}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & \frac{8}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}} & \frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}}-1 & \frac{1}{16} \left(8+\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}\right) & \frac{5 \left(\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}\right)}{22 \pi } \\ \hline \frac{9 \pi }{16} & 101.25 & \frac{1}{2} \sqrt{2+\sqrt{2+\sqrt{2}}} & -\frac{1}{2} \sqrt{2-\sqrt{2+\sqrt{2}}} & -\sqrt{\frac{2+\sqrt{2+\sqrt{2}}}{2-\sqrt{2+\sqrt{2}}}} & -\frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}} & -\sqrt{\frac{2-\sqrt{2+\sqrt{2}}}{2+\sqrt{2+\sqrt{2}}}} & \frac{1}{4} \left(2+\sqrt{2-\sqrt{2+\sqrt{2}}}\right) & \frac{8 \sqrt{2+\sqrt{2+\sqrt{2}}}}{9 \pi } \\ \hline \frac{17 \pi }{30} & 102 & \frac{1}{8} \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(8+\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{68 \pi } \\ \hline \frac{7 \pi }{12} & 105 & \frac{1+\sqrt{3}}{2 \sqrt{2}} & -\frac{\sqrt{3}-1}{2 \sqrt{2}} & -2-\sqrt{3} & -\sqrt{2} \left(1+\sqrt{3}\right) & \sqrt{2} \left(\sqrt{3}-1\right) & \sqrt{3}-2 & \frac{1}{8} \left(4+\sqrt{2} \left(\sqrt{3}-1\right)\right) & \frac{3 \sqrt{2} \left(1+\sqrt{3}\right)}{7 \pi } \\ \hline \frac{3 \pi }{5} & 108 & \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} & \frac{1}{4} \left(1-\sqrt{5}\right) & -\sqrt{5+2 \sqrt{5}} & -1-\sqrt{5} & \frac{1}{\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}} & -\sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{8} \left(3+\sqrt{5}\right) & \frac{5 \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}}{3 \pi } \\ \hline \frac{37 \pi }{60} & 111 & \frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{-1-\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & -1-\frac{2 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & -\frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{2 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}-1 & \frac{1}{32} \left(16+\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}+2 \sqrt{3 \left(5-\sqrt{5}\right)}-\sqrt{6} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{74 \sqrt{2} \pi } \\ \hline \frac{5 \pi }{8} & 112.5 & \frac{\sqrt{2+\sqrt{2}}}{2} & -\frac{1}{2} \sqrt{2-\sqrt{2}} & -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}} & -\frac{2}{\sqrt{2-\sqrt{2}}} & \frac{2}{\sqrt{2+\sqrt{2}}} & -\sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}} & \frac{1}{4} \left(2+\sqrt{2-\sqrt{2}}\right) & \frac{4 \sqrt{2+\sqrt{2}}}{5 \pi } \\ \hline \frac{19 \pi }{30} & 114 & \frac{1}{8} \left(1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)\right) & -\frac{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}-\sqrt{2 \left(5-\sqrt{5}\right)}} & -\frac{8}{\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{8}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(8-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right)}{76 \pi } \\ \hline \frac{13 \pi }{20} & 117 & \frac{1}{8} \left(\sqrt{2} \left(\sqrt{5}-1\right)+2 \sqrt{5+\sqrt{5}}\right) & \frac{1}{8} \left(\sqrt{2} \left(\sqrt{5}-1\right)-2 \sqrt{5+\sqrt{5}}\right) & 1-\frac{4 \sqrt{5+\sqrt{5}}}{\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}} & -\frac{8}{\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}} & \frac{8}{-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}} & 1+\frac{4 \sqrt{5+\sqrt{5}}}{\sqrt{2}-\sqrt{10}-2 \sqrt{5+\sqrt{5}}} & \frac{1}{16} \left(8+\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}\right) & \frac{5 \left(-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}\right)}{26 \pi } \\ \hline \frac{2 \pi }{3} & 120 & \frac{\sqrt{3}}{2} & -\frac{1}{2} & -\sqrt{3} & -2 & \frac{2}{\sqrt{3}} & -\frac{1}{\sqrt{3}} & \frac{3}{4} & \frac{3 \sqrt{3}}{4 \pi } \\ \hline \frac{41 \pi }{60} & 123 & \frac{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & -\frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{2 \sqrt{3} \left(\sqrt{5}-1\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}-1 & -\frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & -\frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & -1-\frac{2 \left(\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{32} \left(16+\sqrt{2} \left(\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right)+\sqrt{2} \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)\right) & -\frac{15 \left(1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{82 \sqrt{2} \pi } \\ \hline \frac{11 \pi }{16} & 123.75 & \frac{1}{2} \left(\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}\right) & \frac{1}{2} \left(-\sqrt{2-\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right) & \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{ 2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & -\frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{2}{\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}}{\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{ 2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}} & \frac{1}{4} \left(2+\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right) & \frac{8 \left(\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}-\sqrt{2+\sqrt{2+\sqrt{2}}}\right)}{11 \pi } \\ \hline \frac{7 \pi }{10} & 126 & \frac{1}{4} \left(1+\sqrt{5}\right) & -\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} & -\sqrt{1+\frac{2}{\sqrt{5}}} & -\frac{1}{\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}} & \sqrt{5}-1 & -\sqrt{5-2 \sqrt{5}} & \frac{1}{2} \left(1+\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}\right) & \frac{5 \left(1+\sqrt{5}\right)}{14 \pi } \\ \hline \frac{43 \pi }{60} & 129 & \frac{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & -\frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & -\frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & 1-\frac{2 \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1}{32} \left(16+\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}-2 \sqrt{3 \left(5-\sqrt{5}\right)}+\sqrt{6} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{86 \sqrt{2} \pi } \\ \hline \frac{11 \pi }{15} & 132 & \frac{1}{8} \left(\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(9-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{88 \pi } \\ \hline \frac{3 \pi }{4} & 135 & \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & -1 & -\sqrt{2} & \sqrt{2} & -1 & \frac{1}{4} \left(2+\sqrt{2}\right) & \frac{2 \sqrt{2}}{3 \pi } \\ \hline \frac{23 \pi }{30} & 138 & \frac{1}{8} \left(1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(\sqrt{3}-\sqrt{15}-\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & -\frac{8}{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{8}{1-\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(\sqrt{3} \left(\sqrt{5}-1\right)+2 \left(4+\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}\right)\right) & -\frac{15 \left(-1+\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{92 \pi } \\ \hline \frac{47 \pi }{60} & 141 & \frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & 1-\frac{2 \left(\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & -\frac{8 \sqrt{2}}{-1-\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1}{32} \left(16-\sqrt{2}+\sqrt{6}+\sqrt{10} \left(\sqrt{3}-1\right)+2 \sqrt{5-\sqrt{5}}+2 \sqrt{3 \left(5-\sqrt{5}\right)}\right) & \frac{15 \left(1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)\right)}{94 \sqrt{2} \pi } \\ \hline \frac{4 \pi }{5} & 144 & \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}} & \frac{1}{4} \left(-1-\sqrt{5}\right) & -\sqrt{5-2 \sqrt{5}} & 1-\sqrt{5} & \frac{1}{\sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}} & -\sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{8} \left(5+\sqrt{5}\right) & \frac{5 \sqrt{\frac{5}{8}-\frac{\sqrt{5}}{8}}}{4 \pi } \\ \hline \frac{13 \pi }{16} & 146.25 & \frac{1}{2} \left(\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right) & \frac{1}{2} \left(\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}\right) & \frac{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}}{\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{ 2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}} & \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}} & \frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}-\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}}{\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{ 2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}} & \frac{1}{4} \left(2-\sqrt{2+\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2+\sqrt{2+\sqrt{2}}\right)}\right) & \frac{8 \left(\sqrt{2-\sqrt{2+\sqrt{2}}}+\sqrt{\left(2+\sqrt{2}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\right)}{13 \pi } \\ \hline \frac{49 \pi }{60} & 147 & \frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & -1-\frac{2 \left(\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{2 \sqrt{3} \left(\sqrt{5}-1\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}}-1 & \frac{1}{32} \left(16+\sqrt{2} \left(\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right)+\sqrt{2} \left(-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)\right) & \frac{15 \left(-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{98 \sqrt{2} \pi } \\ \hline \frac{5 \pi }{6} & 150 & \frac{1}{2} & -\frac{\sqrt{3}}{2} & -\frac{1}{\sqrt{3}} & -\frac{2}{\sqrt{3}} & 2 & -\sqrt{3} & \frac{1}{4} \left(2+\sqrt{3}\right) & \frac{3}{5 \pi } \\ \hline \frac{17 \pi }{20} & 153 & \frac{1}{8} \left(2 \sqrt{5+\sqrt{5}}-\sqrt{2} \left(\sqrt{5}-1\right)\right) & \frac{1}{8} \left(-\sqrt{2} \left(\sqrt{5}-1\right)-2 \sqrt{5+\sqrt{5}}\right) & 1+\frac{4 \sqrt{5+\sqrt{5}}}{\sqrt{2}-\sqrt{10}-2 \sqrt{5+\sqrt{5}}} & \frac{8}{\sqrt{2}-\sqrt{10}-2 \sqrt{5+\sqrt{5}}} & \frac{8}{2 \sqrt{5+\sqrt{5}}-\sqrt{2} \left(\sqrt{5}-1\right)} & 1-\frac{4 \sqrt{5+\sqrt{5}}}{\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}} & \frac{1}{16} \left(8-\sqrt{2}+\sqrt{10}+2 \sqrt{5+\sqrt{5}}\right) & \frac{5 \left(\sqrt{2}-\sqrt{10}+2 \sqrt{5+\sqrt{5}}\right)}{34 \pi } \\ \hline \frac{13 \pi }{15} & 156 & \frac{1}{8} \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right) & \frac{1}{8} \left(-1-\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{\sqrt{2 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & -\frac{8}{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{8}{\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}} & -\frac{1+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}-\sqrt{2 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(9+\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{104 \pi } \\ \hline \frac{7 \pi }{8} & 157.5 & \frac{\sqrt{2-\sqrt{2}}}{2} & -\frac{1}{2} \sqrt{2+\sqrt{2}} & -\sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}} & -\frac{2}{\sqrt{2+\sqrt{2}}} & \frac{2}{\sqrt{2-\sqrt{2}}} & -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}} & \frac{1}{4} \left(2+\sqrt{2+\sqrt{2}}\right) & \frac{4 \sqrt{2-\sqrt{2}}}{7 \pi } \\ \hline \frac{53 \pi }{60} & 159 & \frac{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & -\frac{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}{8 \sqrt{2}} & \frac{2 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)}-1 & -\frac{8 \sqrt{2}}{1+\sqrt{5}-\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{8 \sqrt{2}}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & -1-\frac{2 \left(\sqrt{3} \left(1+\sqrt{5}\right)-\sqrt{2 \left(5-\sqrt{5}\right)}\right)}{1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)} & \frac{1}{32} \left(16+\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}+2 \sqrt{3 \left(5-\sqrt{5}\right)}+\sqrt{6} \left(1+\sqrt{5}\right)\right) & \frac{15 \left(1+\sqrt{5}+\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{6 \left(5-\sqrt{5}\right)}-\sqrt{3} \left(1+\sqrt{5}\right)\right)}{106 \sqrt{2} \pi } \\ \hline \frac{9 \pi }{10} & 162 & \frac{1}{4} \left(\sqrt{5}-1\right) & -\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} & -\sqrt{1-\frac{2}{\sqrt{5}}} & -2 \sqrt{\frac{2}{5+\sqrt{5}}} & 1+\sqrt{5} & -\sqrt{5+2 \sqrt{5}} & \frac{1}{2} \left(1+\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}\right) & \frac{5 \left(\sqrt{5}-1\right)}{18 \pi } \\ \hline \frac{11 \pi }{12} & 165 & \frac{\sqrt{3}-1}{2 \sqrt{2}} & -\frac{1+\sqrt{3}}{2 \sqrt{2}} & \sqrt{3}-2 & -\sqrt{2} \left(\sqrt{3}-1\right) & \sqrt{2} \left(1+\sqrt{3}\right) & -2-\sqrt{3} & \frac{1}{8} \left(4+\sqrt{2}+\sqrt{6}\right) & \frac{3 \sqrt{2} \left(\sqrt{3}-1\right)}{11 \pi } \\ \hline \frac{14 \pi }{15} & 168 & \frac{1}{8} \left(\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right) & \frac{1}{8} \left(1-\sqrt{5}-\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & -\frac{8}{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8}{\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{-1+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}}{\sqrt{3} \left(\sqrt{5}-1\right)-\sqrt{2 \left(5+\sqrt{5}\right)}} & \frac{1}{16} \left(7+\sqrt{5}+\sqrt{6 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(\sqrt{3}-\sqrt{15}+\sqrt{2 \left(5+\sqrt{5}\right)}\right)}{112 \pi } \\ \hline \frac{15 \pi }{16} & 168.75 & \frac{1}{2} \sqrt{2-\sqrt{2+\sqrt{2}}} & -\frac{1}{2} \sqrt{2+\sqrt{2+\sqrt{2}}} & -\sqrt{\frac{2-\sqrt{2+\sqrt{2}}}{2+\sqrt{2+\sqrt{2}}}} & -\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}} & \frac{2}{\sqrt{2-\sqrt{2+\sqrt{2}}}} & -\sqrt{\frac{2+\sqrt{2+\sqrt{2}}}{2-\sqrt{2+\sqrt{2}}}} & \frac{1}{4} \left(2+\sqrt{2+\sqrt{2+\sqrt{2}}}\right) & \frac{8 \sqrt{2-\sqrt{2+\sqrt{2}}}}{15 \pi } \\ \hline \frac{19 \pi }{20} & 171 & \frac{1}{8} \left(\sqrt{2} \left(1+\sqrt{5}\right)-2 \sqrt{5-\sqrt{5}}\right) & \frac{1}{8} \left(-2 \sqrt{5-\sqrt{5}}-\sqrt{2} \left(1+\sqrt{5}\right)\right) & \frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}}-1 & -\frac{8}{\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}} & \frac{8}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & -1-\frac{4 \sqrt{5-\sqrt{5}}}{\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}} & \frac{1}{16} \left(8+\sqrt{2}+\sqrt{10}+2 \sqrt{5-\sqrt{5}}\right) & \frac{5 \left(\sqrt{2}+\sqrt{10}-2 \sqrt{5-\sqrt{5}}\right)}{38 \pi } \\ \hline \frac{29 \pi }{30} & 174 & \frac{1}{8} \left(-1-\sqrt{5}+\sqrt{6 \left(5-\sqrt{5}\right)}\right) & -\frac{1}{4} \sqrt{\frac{1}{2} \left(5-\sqrt{5}\right)}-\frac{1}{8} \sqrt{3} \left(1+\sqrt{5}\right) & \frac{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}}{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}} & -\frac{8}{\sqrt{2 \left(5-\sqrt{5}\right)}+\sqrt{3} \left(1+\sqrt{5}\right)} & -\frac{8}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}}{1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}} & \frac{1}{16} \left(8+\sqrt{3}+\sqrt{15}+\sqrt{2 \left(5-\sqrt{5}\right)}\right) & -\frac{15 \left(1+\sqrt{5}-\sqrt{6 \left(5-\sqrt{5}\right)}\right)}{116 \pi } \\ \hline \frac{59 \pi }{60} & 177 & \frac{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & \frac{-1+\sqrt{3}+\sqrt{5}-\sqrt{15}-\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}}{8 \sqrt{2}} & 1+\frac{-2 \sqrt{3} \left(\sqrt{5}-1\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & -\frac{8 \sqrt{2}}{1-\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}+\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{8 \sqrt{2}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & 1+\frac{-2 \sqrt{3} \left(\sqrt{5}-1\right)-2 \sqrt{2 \left(5+\sqrt{5}\right)}}{-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}} & \frac{1}{32} \left(16+\sqrt{2}-\sqrt{10}+\sqrt{6} \left(\sqrt{5}-1\right)+2 \sqrt{5+\sqrt{5}}+2 \sqrt{3 \left(5+\sqrt{5}\right)}\right) & \frac{15 \left(-1+\sqrt{5}+\sqrt{3} \left(\sqrt{5}-1\right)+\sqrt{2 \left(5+\sqrt{5}\right)}-\sqrt{6 \left(5+\sqrt{5}\right)}\right)}{118 \sqrt{2} \pi } \\ \hline \pi & 180 & 0 & -1 & 0 & -1 & 未定義 & 未定義 & 1 & 0 \\ \hline \end{array} $$

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