How to solve a problem by making it more complicated

Often a good first step in solving a mathematical problem is to find a simplified or special-case version of it, solve that, then see if you can generalise.

Sometimes, oddly, the opposite works. You can solve a problem by finding a more complicated version of it, solving the more complicated version, and then tracking back to the original version.

Here is an example.

so the integral we wanted, f(1), equals f(0), which is 2π.