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