四十二角形
cos  2 π 42 = cos  2 π 3 ⋅ 14 = 1 2 ⋅ ( cos  2 π 14 + i ⋅ sin  2 π 14 3 + cos  2 π 14 − i ⋅ sin  2 π 14 3 ) = 1 2 ⋅ 3 ( 20 + 2 28 − 84 i 3 3 + 2 28 + 84 i 3 3 ) 12 + i ⋅ 3 ( 28 − 2 28 − 84 i 3 3 − 2 28 + 84 i 3 3 ) 12 3 + 1 2 ⋅ 3 ( 20 + 2 28 − 84 i 3 3 + 2 28 + 84 i 3 3 ) 12 − i ⋅ 3 ( 28 − 2 28 − 84 i 3 3 − 2 28 + 84 i 3 3 ) 12 3 {\displaystyle {\begin{aligned}\cos {\frac {2\pi }{42}}=&\cos {\frac {2\pi }{3\cdot 14}}\\=&{\frac {1}{2}}\cdot \left({\sqrt[{3}]{\cos {\frac {2\pi }{14}}+i\cdot \sin {\frac {2\pi }{14}}}}+{\sqrt[{3}]{\cos {\frac {2\pi }{14}}-i\cdot \sin {\frac {2\pi }{14}}}}\right)\\=&{\frac {1}{2}}\cdot {\sqrt[{3}]{{\tfrac {\sqrt {3\left(20+2{\sqrt[{3}]{28-84i{\sqrt {3}}}}+2{\sqrt[{3}]{28+84i{\sqrt {3}}}}\right)}}{12}}+i\cdot {\tfrac {\sqrt {3\left(28-2{\sqrt[{3}]{28-84i{\sqrt {3}}}}-2{\sqrt[{3}]{28+84i{\sqrt {3}}}}\right)}}{12}}}}+{\frac {1}{2}}\cdot {\sqrt[{3}]{{\tfrac {\sqrt {3\left(20+2{\sqrt[{3}]{28-84i{\sqrt {3}}}}+2{\sqrt[{3}]{28+84i{\sqrt {3}}}}\right)}}{12}}-i\cdot {\tfrac {\sqrt {3\left(28-2{\sqrt[{3}]{28-84i{\sqrt {3}}}}-2{\sqrt[{3}]{28+84i{\sqrt {3}}}}\right)}}{12}}}}\end{aligned}}}