四十二角形
αの値((-1+√21)/2)を代入して、整理すると
cos  2 π 42 = − 1 + 21 + − 154 − 30 21 + ( 42 3 + 18 7 ) i 3 + − 154 − 30 21 − ( 42 3 + 18 7 ) i 3 12 {\displaystyle \cos {\frac {2\pi }{42}}={\frac {-1+{\sqrt {21}}+{\sqrt[{3}]{-154-30{\sqrt {21}}+\left(42{\sqrt {3}}+18{\sqrt {7}}\right)i}}+{\sqrt[{3}]{-154-30{\sqrt {21}}-\left(42{\sqrt {3}}+18{\sqrt {7}}\right)i}}}{12}}}