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Let $A = \left\{ \theta \in \left( -\frac{\pi}{2}, \pi \right) : \frac{3 + 2i \sin \theta}{1 - 2i \sin \theta} \text{ is purely imaginary} \right\}$. Then the sum of the elements in $A$ is

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The real value of $\alpha$ for which $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely real is

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