If  $k=\sin \pi /18\sin 5\pi /18\sin 7\pi /18$   then the numerical value of k is equal to

$k=\sin \pi /18\sin 5\pi /18\sin 7\pi /18$

$\begin{array}{l}=\sin {10}^{\circ }\sin {50}^{\circ }\sin {70}^{\circ }\\ =\frac{1}{2}\left[\cos {40}^{\circ }-\cos {60}^{\circ }\right]\sin {70}^{\circ }\\ =\frac{1}{2}\cos {40}^{\circ }\sin {70}^{\circ }-\frac{1}{4}\sin {70}^{\circ }\\ =\frac{1}{4}\left[\sin {110}^{\circ }+\sin {30}^{\circ }\right]-\frac{1}{4}\sin {70}^{\circ }\end{array}$

$=\frac{1}{4}\sin \left({180}^{\circ }-{70}^{\circ }\right)+\frac{1}{4}\times \frac{1}{2}-\frac{1}{4}\sin {70}^{\circ }=\frac{1}{8}$