Limits Continuity And Differentiability

Let \(f:(0, \pi) \rightarrow \mathbf{R}\) be a function given by $$f(x)=\left\{\begin{array}{cc}\left(\frac{8}{7}\right)^{\frac{\tan 8 x}{\tan 7 x}}, & 0< x<\frac{\pi}{2} \\ \mathrm{a}-8, & x=\frac{\pi}{2} \\ (1+\mid \cot x)^{\frac{\mathrm{b}}{\mathrm{a}}|\tan x|}, & \frac{\pi}{2} < x < \pi\end{array}\right.$$

where \(\mathrm{a}, \mathrm{b} \in \mathbf{Z}\). If \(f\) is continuous at \(x=\frac{\pi}{2}\), then \(\mathrm{a}^2+\mathrm{b}^2\) is equal to _________.