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:<math>\cos\frac{2\pi}{21} = \cos \left(\frac{2\pi}{3}-\frac{4\pi}{7}\right) </math>
 
[[:en:Trigonometric constants expressed in real radicals#List of trigonometric constants of 2π/n|Trigonometric constants expressed in real radicals]]より
:<math>\cos\frac{2\pi}{21} = \frac{1}{12}\left(\sqrt[3]{154-30\sqrt{21}+42\sqrt{-3}-18\sqrt{-7}}+\sqrt[3]{154-30\sqrt{21}-42\sqrt{-3}+18\sqrt{-7}}+\sqrt{21}+1\right)</math>