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:

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