If sum of all the solutions of the equation
Question:

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

1. $\frac{13}{9}$

2. $\frac{8}{9}$

3. $\frac{20}{9}$

4. $\frac{2}{3}$

Correct Option: 1

Solution: