Let A = {θ ∈ (0,2π): 1+2i sinθ / 1- i sinθ is purely imaginary}.

Question

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

(1) π

(2) 3π 

(3) 4π 

(4) 2π

Answer 1

Correct option is (3) 4π