Problem 1.

1. Evaluate the integral ${\int }_0^{2\pi }\left(\frac{d^{}\left(\theta \right)}{2-\sin \left(\theta \right)}\right)$ using residues.
   Hint: pick $\gamma =$unit circle $z=e^{𝑖\theta },$ then $\sin \left(\theta \right)=\frac{1}{2𝑖}(z-\frac{1}{z})$.