  [*Subcase*]{} 0.0. One of $\alpha, \beta$, say $\alpha$, is a cusp and the other, $\beta$, is an interior generalized simple closed geodesic.  In this case $$\begin{aligned} {\rm Gap}(\Delta_{0};\alpha, \beta) &=& 0 \tan^{-0} \left ( \frac {\sin \frac{\theta}{0}}{\cos\frac{\theta}{0}+ \exp\frac{|\