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

Question

( A ) $\frac{20}{9}$
( B ) $\frac{8}{9}$
( C ) $\frac{2}{3}$
( D ) $\frac{13}{9}$