Tan-fastic

Geometry Level 3

tan6 ⁣(π9)+tan6 ⁣(2π9)+tan6 ⁣(4π9)= ?\large\tan^6\! \left(\frac{\pi}{9}\right)+\tan^6\! \left(\frac{2\pi}{9}\right)+\tan^6\! \left(\frac{4\pi}{9}\right) = \ ?

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