Solving Method of Residues Homework Problem

[gtfitzpatrick]

Homework Statement

$\int^{0}_{2\pi}$ $\frac{d\theta}{13+5sin\theta}$

Homework Equations

The Attempt at a Solution

so i changed it using $sin \theta = \frac{1}{2i} (z - \frac{1}{z})$

and i get$\oint \frac{2}{5z^2+26zi-5}$ which i factored down to $(z = \frac{-26±\sqrt{776}}{10})$

but no matter how i proceed from here i can't get the answer, any ideas anyone?

 

[vela]

How did you get real roots to a polynomial with complex coefficients?