Evaluate the integral $ \int_0^{2\pi}\frac{1}{3-2\cos \theta +\sin\theta}\,\mathrm d\theta. $
This must be solved by using $d \theta = dz/(iz)$ and transforming $\sin, \cos$ to complex form, but I am stuck after transforming it. It is now $\frac{1}{(2i+1)z^2 - 6i z + (2i+1)}$ I don't know how to complete it now to find the singularities and solve by the residue theorem.