JEE Math Practice Question

If $$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\begin{matrix} 0 & {\cos x} & { - \sin x} \\ {\sin x} & 0 & {\cos x} \\ {\cos x} & {\sin x} & 0 \\ \end{matrix} } \right| = 0} \right\},$$ then $$\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $$ is equal to :

1. A.$$4 + 2\sqrt 3 $$
2. B.$$ - 2 + \sqrt 3 $$
3. C.$$ - 2 - \sqrt 3 $$
4. D.$$-\,\,4 - 2\sqrt 3 $$