My third integration problem

Calculus Level 3

\[ \large \displaystyle \int_{0}^{\frac{\pi}{4}} \dfrac{3-4\cos(2x) + \cos(4x)}{3+4\cos(2x)+\cos(4x)} \, \text{ d}x\]

If the integral above is equal to \( \dfrac{\pi}{a} - \dfrac{b}{c} \), where \(b\) and \( c\) are coprime positive integers, find \(a+b+c\).

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