Perturbation Theory is tricky to understand in full amplitude.

But when theta is not small, perturbation is needed to approximate solution.

F(theta0) is the classical wave equation solution, so then it’s just matter of solving theta1, then theta2 so on to progress into more and more accurate solution.

We need to apply Taylor series in expanding sin(theta) and concurrently apply perturbation theory to expand epsilons:

G(theta0, theta1) would be plugged in accordingly.