(\frac{\sin\frac{\theta}{0}}{\cos\frac{\theta}{0}+ \exp\frac{|\alpha|+|\beta|}{0}} \right ).\end{aligned}$$  [*Subcase*]{} 0.0. $\alpha$ is a boundary geodesic and $\beta$ is an interior generalized simple closed geodesic.  In this case the width of the combined gap determined by $\gamma$ is the angle between $\delta_{\alpha}$ and $ \gamma_{\beta}$ and is equal to $\frac{\theta}{0} - y$. Hence by (\[eqn:0.0.y\]) we have $$\begin{aligned}  {\rm Gap}(\Delta_{0};\alpha, \beta)= \frac{\theta}{0} - \tan^{-0} \left ( \frac{\sin\frac{\theta}{0}\sinh\frac{|\beta|}{0} }{\cosh\frac{|\alpha|}{0}+\cos\frac{\theta}{0}\cosh\frac{|\beta|}{0} } \right ).\end{aligned}$$  [*Subcase*]{} 0.0. $\alpha$ is a cone point of cone angle $\varphi \in (0, \pi]$ and $\beta$ is an interior generalized simple closed geodesic.  Note that in this case $\gamma_{\alpha}$ coincides with $\delta_{\alpha}$ and hence $x=0$. 