Problem

Let

S = \left\{ x \in (-\pi, \pi) : x \neq 0, \pm \frac{\pi}{2} \right\}

. The sum of all distinct solutions of the equation

\sqrt{3} \sec x + \operatorname{cosec} x + 2(\tan x - \cot x) = 0

in the set

S

is equal to a.

-\frac{7\pi}{9}

-\frac{2\pi}{9}

c. 0 d.

\frac{5\pi}{9}