Express sin(5theta) in terms of sin(theta) and powers of sin(theta) only.

Consider the expression (cos(theta) + i*sin(theta))⁵ . (Where theta a real parameter).By De Moirve's theorem, we know this expression is equivalent to cos(5theta) + i sin(5theta).We can also apply the binomial expansion to this expression and sort into real and imaginary components.We can then equate these two expressions we have found and compare imaginary components to obtain the required solution.This is best written out by hand.