Good Bye 2015 - 2!

Geometry Level 5

\[\large \dfrac{3 \tan^4 \left( \dfrac\pi7 \right) + 1}{35+ \tan^4\left( \dfrac\pi7 \right)} = \dfrac{A}{B} \tan^{C} \left( \dfrac\pi7 \right) \]

Given that the equation above is true for positive integers \(A,B,C\) with \(A,B\) coprime, find the value of \(A+B+C\).

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