How would I compute:

$\displaystyle I=\int_{2\pi }^{0}\frac{4d\theta }{2 cos\theta + 3 sin\theta + 2i}$

I have tried finding the poles by changing the values into complex values

where $\displaystyle z=e^{i\theta }$

$\displaystyle 2cos\theta =z+\frac{1}{z}$

$\displaystyle 2sin\theta =-i({z-\frac{1}{z}})$

I have concluded

$\displaystyle I=\oint \frac{\frac{4dz}{iz}}{(z+\frac{1}{z})-\frac{3i}{2}(z-\frac{1}{z})+2i}$

Could someone tell me if this correct and I cant find the poles cause I cant find anyway of factorising! Thanks in advance!