Good Bye 2015 - 2!

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

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