百八十角形
2 cos  2 π 180 ⋅ 2 cos  122 π 180 + 2 cos  122 π 180 ⋅ 2 cos  118 π 180 + 2 cos  118 π 180 ⋅ 2 cos  2 π 180 = − 3 2 cos  2 π 180 ⋅ 2 cos  122 π 180 ⋅ 2 cos  118 π 180 = 2 cos  2 π 60 {\displaystyle {\begin{aligned}&2\cos {\frac {2\pi }{180}}\cdot 2\cos {\frac {122\pi }{180}}+2\cos {\frac {122\pi }{180}}\cdot 2\cos {\frac {118\pi }{180}}+2\cos {\frac {118\pi }{180}}\cdot 2\cos {\frac {2\pi }{180}}=-3\\&2\cos {\frac {2\pi }{180}}\cdot 2\cos {\frac {122\pi }{180}}\cdot 2\cos {\frac {118\pi }{180}}=2\cos {\frac {2\pi }{60}}\\\end{aligned}}}
解と係数の関係より
u 3 − 3 u − 2 cos  2 π 60 = 0 {\displaystyle u^{3}-3u-2\cos {\frac {2\pi }{60}}=0}
三次方程式を解くと