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JEE Math Practice Question

The sum of all possible values of $$\theta \in[-\pi, 2 \pi]$$, for which $$\frac{1+i \cos \theta}{1-2 i \cos \theta}$$ is purely imaginary, is equal to :

  1. A.$$4 \pi$$
  2. B.$$3 \pi$$
  3. C.$$2 \pi$$
  4. D.$$5 \pi$$

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