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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