# Log-sine

Calculus Level 5

$\large \int_0^{2\pi} x^2 \left( \ln \left( 2 \sin \dfrac x2 \right) \right)^2 \, dx = \dfrac AC \pi^B$

If the equation above holds true for positive integers $$A,B$$ and $$C$$ such that $$A,B$$ are coprime, find $$A+B+C$$.

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