I don't know the whole solution yet but start on the left hand side with
What do you get?
((1+sin(15x))(1-sin(x))/(1-sin(5 x))(1+sin(3x)))=
{16(sinx)^4 - 8(sinx)^3 - 16(sinx)^2 + 8sinx +1}^2
Any idea that help in solving this equality is appreciated.