# Who's up to the challenge? 60

Calculus Level 5

$\int _{ 0 }^{ \pi }{ \left( \ln { \left[ \left( 2\sin { \frac { x }{ 2 } } \right) \left( 2\cos { \frac { x }{ 2 } } \right) ^{ 2 } \right] } \right) ^{ 3 }\, dx } =-A\pi \zeta (B)$

If the equation above holds true for positive integers $$A$$ and $$B$$, then find $$A\times B$$.

Notation: $$\zeta(\cdot)$$ denotes the Riemann zeta function.

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