Mathematics

Problem

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

[0, \pi]

k\pi

, then

k

is equal to (1)

\frac{2}{3}

(2)

\frac{13}{9}

(3)

\frac{8}{9}

(4)

\frac{20}{9}