We prepare integral from 0 to 2 Pi of 1/(2+cos(theta)) for integration in the complex plane.

We complete the integration introduced in part 1, using Cauchy's residue theorem.

We attempt to evaluate an integral that is not well-defined and investigate how this problem manifests itself in the complex contour version of the integral.

We complete the integration introduced in part 3, using Cauchy's residue theorem.