\[\theta_{n+1}=\theta_{n}-\frac{x_{t} \sin 2 \theta_{n}-2 y_{t} \cos ^{2} \theta_{n}-g x_{t}^{2} / v_{0}^{2}}{2 x_{t} \cos 2 \theta_{n}+2 y_{t} \sin 2 \theta_{n}}\] Then plug this \(\theta_{0}\) into ...\[\theta_{n+1}=\theta_{n}-\frac{x_{t} \sin 2 \theta_{n}-2 y_{t} \cos ^{2} \theta_{n}-g x_{t}^{2} / v_{0}^{2}}{2 x_{t} \cos 2 \theta_{n}+2 y_{t} \sin 2 \theta_{n}}\] Then plug this \(\theta_{0}\) into the right-hand side, which returns \(\theta_{1}\); for the next iteration, plug this \(\theta_{1}\) into the right-hand side, which returns \(\theta_{2}\), etc.
