\[ \large I=\int _{ 0 }^{ \frac { \pi }{ 4 } }{ \frac { { x }^{ 2 } }{ { (x\sin { x } +\cos { x } ) }^{ 2 } } \, dx } =\frac { a-b\pi }{ a+b\pi } \]

The equation above holds true for coprime positive integers \(a\) and \(b\). Find \(a+b\).

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