Trigonometric Tangents

Geometry Level 4

x=tan8π24+tan85π24+tan87π24+tan811π24\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 xx is an integer, find the sum of the digits of xx.

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