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Let the maximum value of sinxcosx\sin x \cos xsinxcosx for x∈Rx \in \mathbb{R}x∈R be MMM. If the value of xxx for which sinxcosx\sin x \cos xsinxcosx is maximum, where 0<x<π0< x < \pi0<x<π, can be expressed as AπB\dfrac{A\pi}{B}BAπ for positive coprime integers AAA and BBB, compute M+A+BM+A+BM+A+B.
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