Sine Product

Geometry Level 3

\[\large\sin\left(\dfrac{\pi}{34}\right)\sin\left(\dfrac{9\pi}{34}\right)\sin\left(\dfrac{13\pi}{34}\right)\sin\left(\dfrac{15\pi}{34}\right)\]

If the value of the expression above can be represented by \(\dfrac{p}q\), where \(p\) and \(q\) are coprime positive integers, compute \(p+q\).

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