9.1.3. Find the minimum value of the function $f(x)=\operatorname{tg}^{2} x-4 \operatorname{tg} x-8 \operatorname{ctg} x+4 \operatorname{ctg}^{2} x+5$ on the interval $\left(\frac{\pi}{2} ; \pi\right)$.
Answer: $9+8 \sqrt{2} \approx 20.31$.