SineCosine at its pinnacle

Geometry Level 2

Let the maximum value of sinxcosx\sin x \cos x for xRx \in \mathbb{R} be MM. If the value of xx for which sinxcosx\sin x \cos x is maximum, where 0<x<π0< x < \pi, can be expressed as AπB\dfrac{A\pi}{B} for positive coprime integers AA and BB, compute M+A+BM+A+B.

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