From cosine to sine

Geometry Level 1

Suppose

cosθ=35,sin2θ=ab,\cos\theta = \frac{3}{5},\quad \sin2\theta = \frac{a}{b},

where 0<θ<π20<\theta <\frac{\pi}{2} with aa and bb coprime positive integers.

What is the value of a+b?a+b?

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