I've found that in the first part of the question

$\displaystyle sin^5\theta = \frac{1}{16}(sin5\theta-5sin3\theta+10sin\theta) $

Now I have to solve $\displaystyle sin5\theta-5sin3\theta+6sin\theta = 0 $ for theta

I can see straight away that 0 and multiples of pi are my solutions,

But I don't know how to do this problem in a methodical way.

I thought there would be substitution involved but I can't see how.

Help appreciated.