For a course in Complex Analysis we're tasked to find the integral of
\begin{align\*}
\int\_0^{2 \pi} (\sin\theta)^{2014} d \theta
\end{align\*}
but I'm a bit stumped so far on how to do this.

What I've done so far: 

* First I tried to replace $ \sin \theta$ by $\frac{e^{i \theta} - e^{-i \theta}}{2i}$, but you still have this weird term $(e^{i \theta} - e^{-i \theta})^{2014}$ to deal with, so I guess that's not the correct way.
* Secondly I thought about intepreting this as the imaginary part of $e^{i \theta}$, but I get stuck on the 2014 power, so this method presents problems as well.

If anyone could point me in the right direction I would be very grateful, thank you!