# Prime Power Roots

Algebra Level 4

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

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 $$a, b$$ are coprime positive integers, compute $$a+b$$.

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