Please read the screen captured image for the problem. I have actually solved the problem however I was not able to use the hint by the author. Give another hint or solve the problem USING THE HINT.
Here is how I did it. Do note all angles are in degrees.
$$\sin10^{\circ}\sin(60^{\circ}-10^{\circ})\sin(60^{\circ}+10^{\circ})=(3\sin10^{\circ}-4(\sin10^{\circ})^3)/4=\sin(3\cdot10^{\circ})/4=1/8.$$
I used triple angle formula which at this point has not been introduced and nowhere in my solution have i used the hint.