prove that sin10.sin30.sin50.sin70 = 1/16

well, I grouped together to make this

(sine10.sin50)(sin30.sin70)

Since 10 + 50 = 60 , and used the identity sinA.sinB = (cos(a-b)-cos(a+b))/2

and got the answer in terms of cos40 after further simplification...

problem is I don't know what cos40 is... Although I could find it out as 40*3 = 120

and cos(3*40)=cos 120 and then simply using cos3A = 4cos^3(A) - 3cosA

but then I will have to simplify an annoying cubic equation...please help, do suggest an easier method..