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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