# Triple Triple Angle Identity

Geometry Level 5

$\dfrac{\sin(9x)}{3\sin(3x)} = \left(1 - \frac{\sin^2(x)}{\sin^2(p)}\right)\left(1 - \frac{\sin^2(x)}{\sin^2(q)}\right)\left(1 - \frac{\sin^2(x)}{\sin^2(r)}\right)$

Above shows a trigonometric identity with constants $p,q$ and $r$ such that $0 \leq p,q,r\leq \frac \pi2$. If $p + q + r = \dfrac AB \pi$ for coprime positive integers $A$ and $B$, find the value of $A+B$.

Bonus: Generalize the trigonometric identity.

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