\(\begin{equation} \alpha_{n+1}-\alpha_n = \{ \begin{array}{cc} -2 \theta_n - \pi,\; for \; \alpha_n>0 \;and\; \alpha_{n+1}<0\\ -2 \theta_n + \pi,\; else\\ \end{array} \end{equation}\)
\(\begin{equation} \beta_{n+1}= \{ \begin{array}{cc} \frac{\pi}{2} - \theta_n - \alpha_n - 2 \pi,\; for \; \alpha_n>0 \;and\; \beta_{n+1}<0\\ \frac{\pi}{2} - \theta_n - \alpha_n,\; else\\ \end{array} \end{equation}\)
Initial conditions \(\alpha_n\) and \(\beta_n\):