`sin(pi/18)*sin(5pi/18)*sin(7pi/18)`

Explanation

`\sin \(pi / 8) \sin 5 \pi / 18 \sin 7 \pi / 18`


`=\sin 10^{\circ} \sin 50^{\circ} \sin 70^{\circ}`


`=\frac{1}{2}[\cos 40^{\circ}-\cos 60^{\circ}\] \sin 70^{\circ}`


`=\frac{1}{2} \cos 40^{\circ} \sin 70^{\circ}-\frac{1}{4} \sin 70^{\circ}`


`=\frac{1}{4}[\sin 110^{\circ}+\sin 30^{\circ}\]-\frac{1}{4} \sin 70^{\circ}`


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