Please fix this residue integration

[geft]

$$\int_{0}^{2\pi} \frac{d\theta}{5 - 4sin\theta}$$
$$= \oint_{C} \frac{dz/iz}{5 - \frac{2z}{i} - \frac{2}{iz}}$$
$$= - \oint_{C} \frac{dz}{2z^{2} - 5iz - 2}$$
$$= - \oint_{C} \frac{dz}{(4z - 8i)(49 - 2i)}$$
$$z_{1} = 2i, z_{2} = \frac{1}{2}$$
$$Res = \left|\frac{1}{4z - 2i} \right|_{z = 2i} = \frac{1}{6i}$$
$$\Rightarrow 2\pi i(\frac{1}{6i})(-1) = \frac{-\pi}{3}$$

The answer is 2pi/3, but I can't seem to get it.

 

[tiny-tim]

hi geft!

(have a pi: π )

isnt it plus 2 on the third line?

 

[geft]

Oh man, I feel so stupid. This has been driving me crazy all day. Thanks a lot! :)