Trigonometry! #109

Geometry Level 3

In \(\Delta ABC\), \(\angle A>\angle B\). If the measures of angles \(A\) and \(B\) satisfy the equation \[3\sin x - 4\sin^{3}x-k=0\] for \(0<k<1\), then find the measure of \(\angle C\).

Express your answer in the form of \(\left(\frac{p\pi}{q}\right)^{C}\) where \(p\) and \(q\) are coprime integers. Enter the value of \(pq\).

This problem is part of the set Trigonometry.

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