SineCosine at its pinnacle

Geometry Level 3

Let the maximum value of \((\sin x \cos x)\) for \(x \in \mathbb{R}\) be \(M\) . If the value of \(x\) for which \((\sin x \cos x)\) is maximum satisfying \(0< x < \pi\) can be expressed as \(\dfrac{A\pi}{B}\) for co-prime integers \(A,B\) , compute \(M+A+B\).

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