If  $a = \sin \frac{\pi }{{18}}\sin \frac{{5\pi }}{{18}}\sin \frac{{7\pi }}{{18}}$ and $x$ is the solution of the equatioin $y = 2\left[ x \right] + 2$ and $y = 3\left[ {x - 2} \right] ,$ where $\left[ x \right]$ denotes the integral part of $x,$ then $a$ is equal to :-

  • A

    $\left[ x \right]$

  • B

    $\frac{1}{{\left[ x \right]}}$

  • C

    $2\left[ x \right]$

  • D

    ${\left[ x \right]^2}$

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