Exponentiating Sine

Algebra Level 3

Suppose θ\theta is an angle strictly between 00 and π2\frac{\pi}{2} such that sin5θ=sin5θ\sin 5\theta = \sin ^5 \theta . The number tan2θ\tan 2\theta can be uniquely written as aba \sqrt{b}, where aa and bb are positive integers, and bb is not divisible by the square of a prime. What is the value of a+ba+b?

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