# Exponentiating Sine

Algebra Level 3

Suppose $$\theta$$ is an angle strictly between $$0$$ and $$\frac{\pi}{2}$$ such that $$\sin 5\theta = \sin ^5 \theta$$. The number $$\tan 2\theta$$ can be uniquely written as $$a \sqrt{b}$$, where $$a$$ and $$b$$ are positive integers, and $$b$$ is not divisible by the square of a prime. What is the value of $$a+b$$?

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