# Soviet Sine

Geometry Level 4

Given acute positive angles $$\alpha$$ and $$\beta$$, which satisfy the following equations:

$3\sin^{2}\alpha+2\sin^{2}\beta=1$ $3\sin2\alpha-2\sin2\beta=0$

If $$\alpha+2\beta$$ can be expressed in the form $$\dfrac{a\pi}{b}$$, where $$a$$ and $$b$$ are relatively prime, then find $$a+b$$.

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