Let f:(0, π) → R be a function given by f(x)= {(8/7)^((tan 8 x)/(tan 7 x)), 0<x<(π)/2; a-8, x=(π)/2; (1+| cot x|)^b/a| tan x|, (π)/2<x<π} where a, b…

Let $\displaystyle f:(0, \pi) \rightarrow \mathbf{R}$ be a function given by $\displaystyle f(x)=\left\{\begin{array}{cc}\left(\frac{8}{7}\right)^{\frac{\tan 8 x}{\tan 7 x}}, & 0<x<\frac{\pi}{2} \\ a-8, & x=\frac{\pi}{2} \\ (1+|\cot x|)^{\frac{b}{a}|\tan x|}, & \frac{\pi}{2}<x<\pi\end{array}\right.$ where $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{Z}$. If $\displaystyle f$ is continuous at $\displaystyle x=\frac{\pi}{2}$, then $\displaystyle \mathrm{a}^2+\mathrm{b}^2$ is equal to $\displaystyle \_\_\_\_$.