HCI Sequence and Series Tutorial Q5

Given that $\text{f}\left( r \right)=\cos 2r\theta $, write $\text{f}\left( r \right)-\text{f}\left( r+1 \right)$ as a product of two sine functions. Use your result to find the sum of the first $n$ terms of the series

$\sin 3\theta +\sin 5\theta +\sin 7\theta +…$