Mathematics

Problem

The sum of all possible value of

\theta \in [-\pi, 2\pi]

, for which

\frac{1 + i\cos\theta}{1 - 2i\cos\theta}

is purely imaginary, is equal to (2024 Main, 8 April II) (a)

4\pi

(e)

3\pi

(b)

5\pi

(d)

2\pi