JEE Math Practice Question

If sum of all the solutions of the equation $$8\cos x.\left( {\cos \left( {{\pi \over 6} + x} \right).\cos \left( {{\pi \over 6} - x} \right) - {1 \over 2}} \right) = 1$$ in [0, $$\pi $$] is k$$\pi $$, then k is equal to

1. A.$${{20} \over 9}$$
2. B.$${2 \over 3}$$
3. C.$${{13} \over 9}$$
4. D.$${{8} \over 9}$$