Using De Moivre's Theorem

Hello,

Doing a practice paper and found this question, not sure what to do:

Quote:

Write down de Moivre's Theorem for n=5. hence show that for $\displaystyle \sin \theta \neq 0$

$\displaystyle \frac{\sin 5 \theta}{\sin \theta} = A cos^4 \theta + B \cos^2 \theta + C$

where A, B, C are constants to be determined.

Deduce the limiting value of $\displaystyle \frac{\sin 5 \theta}{\sin \theta} $ as $\displaystyle \theta $ tends to zero.

I've written de Moivre for n=5:

$\displaystyle (r(\cos \theta + i \sin \theta))^5 = r^5(\cos 5\theta + i \sin 5 \theta)$

But don't know where to go from there, at all.

Thanks