# Prime Power Roots

$\begin{cases} \alpha^3 \beta^5 = 1 \\ \alpha^7 \beta^2 = 1 \end{cases}$

Let $\alpha = \cos \theta_1 + i \sin \theta_1$ and $\beta = \cos \theta_2 + i \sin \theta_2$ be the complex numbers satisfying the system above, where $0 < \theta_1$ and $\theta_2 < \frac{\pi}{2}$.

If $\frac{\theta_1}{\theta_2} = \frac{a}{b}$, where $a$ and $b$ are coprime positive integers, compute $a+b.$

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