In summary, the conversation revolved around finding a solution for the integral \int \frac{1}{(1+a cos(\theta - \phi))^2} d\theta where a is a constant. Suggestions were made to expand the denominator and use the derivative of tan^{-1}{(\theta + \phi)} to simplify the solution, but it was ultimately solved by considering the substitution \theta- \phi=t. Some users suggested using software like Mathematica to solve the integral, while others mentioned using numerical methods or defining it as a new function. Additionally, someone recommended looking into elliptical integrals for more information. Overall, the conversation ended with the suggestion to use the aforementioned substitution for an easier solution.