# 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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