Let A = { 0 ∈ (−π/2, π): 3 + 2i sinθ / 1 − 2i sinθ is purely imaginary } Then the sum of the elements in A is :

Question

Let $A=\left\{0\in\left({-\pi\over2},\pi\right):{3+2i\sin\theta\over1-2i\sin\theta}\text{ is purely imaginary}\right\}$ Then the sum of the elements in $A$ is :

(1) $5\pi\over6$

(2) $2\pi\over3$

(3) $3\pi\over4$

(4) $\pi$