Trigonometric Tangents

Geometry Level 4

\[\large x = \tan^8\dfrac{\pi}{24}+\tan^8\dfrac{5\pi}{24}+\tan^8\dfrac{7\pi}{24}+\tan^8\dfrac{11\pi}{24}\]

Given that \(x\) is an integer, find the sum of the digits of \(x\).

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