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Let $$ S = \left\{x \epsilon (-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\}$$ The sum of all distinct solutions of the equation $$\sqrt{3} \sec x + \cosec x + 2(\tan x - \cot x) = 0$$ in the set S is equal to
$$-\frac{7 \pi}{9}$$
$$-\frac{2 \pi}{9}$$
$$0$$
$$\frac{5 \pi}{9}$$
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