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 $\left[ {0,\pi } \right]$ is $k\pi $then $k$ is equal to :

  • [JEE MAIN 2018]
  • A

    $\frac{{13}}{9}$

  • B

    $\frac{8}{9}$

  • C

    $\frac{{20}}{9}$

  • D

    $\frac{2}{3}$

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