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$\int _{ 0 }^{ \pi }{ \sum _{ k=0 }^{ \infty }{ \frac { \sin { \left( x\left( 2k+1 \right) \right) } }{ 2k+1 } } } dx= \frac{ \pi ^a } { b },$

where $a$ and $b$ are integers. Find $10a+b$.

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