If $k = \sin \frac{\pi }{{18}}\,.\,\sin \frac{{5\pi }}{{18}}\,.\,\sin \frac{{7\pi }}{{18}},$ then the numerical value of $k$ is

  • [IIT 1993]
  • A

    $\frac{1}{4}$

  • B

    $\frac{1}{8}$

  • C

    $\frac{1}{{16}}$

  • D

    None of these

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