(\frac{\sin\frac{\theta}{0}}{\cos\frac{\theta}{0}+ \exp\frac{|\alpha|+|\beta|}{0}} \right ).\end{aligned}$$  [*Subcase*]{} 0.0. One of $\alpha, \beta$, say $\alpha$, is a boundary geodesic and the other, $\beta$, is an interior generalized simple closed geodesic.  In this case $$\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}$$  [*Subcase*]{} 0.0. One of $\alpha, \beta$, say $\alpha$, is a cone point of cone angle $\varphi \in (0,\pi]$ and the other, $\beta$, is an interior generalized simple closed geodesic.  In this case $$\begin{aligned} 