Too Complex! Part- III

Geometry Level 4

sin5θ=5sinθ(1sin2θsin2p)(1sin2θsin2q) \sin 5\theta = 5 \sin \theta \left ( 1 - \frac{\sin^{2} \theta}{\sin ^{2} p} \right) \left( 1 - \frac{\sin^{2} \theta}{\sin ^{2} q} \right)

If the equation above is a trigonometric identities for constants pp and qq such that 0p,qπ2 0 \leq p,q\leq \frac \pi2, find the value of p+qp + q.

Clue: Use the equation z101=0 z^{10} - 1 = 0

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