May be too lengthy

Calculus Level 5

\[\large{\displaystyle \int^{\pi}_{0} \arctan \left(\dfrac{\sin x}{3- \cos x} \right) \sin (3x) \, dx}\]

If the integral above is equal to \( \dfrac AB \pi^C \), where \(A,B\) and \(C\) are positive integers with \(A,B\) coprime, find \(A+B+C\).

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