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JEE Math Practice Question

Let $$A=\left\{\theta \in(0,2 \pi): \frac{1+2 i \sin \theta}{1-i \sin \theta}\right.$$ is purely imaginary $$\}$$. Then the sum of the elements in $$\mathrm{A}$$ is :

  1. A.$$3 \pi$$
  2. B.$$\pi$$
  3. C.$$2 \pi$$
  4. D.$$4 \pi$$

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