In the study of graphical representations of the Ising model I have encountered the following sum for natural numbers $a,b$ such that $b \leq a$
$$ \sum_{\theta \in \{ \frac{ 2 \pi k}{q}, k = 0, \dots , q-1 \}} (-\sin(\theta))^{a-b} \cos(\theta)^b. $$
Does this expression have a closed formula?