# This time the limits have changed!

Calculus Level 5

$\int _{ 0 }^{ \pi /3 }{ x{ \left[ \ln { \left( 2\sin { \left( \dfrac { x }{ 2 } \right) } \right) } \right] }^{ 2 } \, dx } =\dfrac { { A\pi }^{ B } }{ C }$

This equation holds true for positive integers $$A,B,C$$ with $$A$$ and $$C$$ being coprime. Evaluate $$A+B+C$$.

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