sin20°sin40°sin80°
=-1/2(cos60-cos(-20))sin80
=-1/4sin80+1/2cos20*sin80
=-1/4sin80+1/2*1/2(sin100+sin60)
=-1/4sin80+1/4sin100+1/4*(根号3/2)
=(根号3/8)
sin20*sin40*sin80
=sin20*cos20*sin40*sin80/cos20
=sin40*sin40*sin80/2sin160
=sin40*sin40/4cos80
=1/4(cot40^2-1)