$9 \cdot 60$ Let $x_{1}, x_{2}, x_{3}, x_{4}$ all be positive numbers, and $x_{1}+x_{2}+x_{3}+x_{4}=\pi$, find the minimum value of the expression
$$\left(2 \sin ^{2} x_{1}+\frac{1}{\sin ^{2} x_{1}}\right)\left(2 \sin ^{2} x_{2}+\frac{1}{\sin ^{2} x_{2}}\right)\left(2 \sin ^{2} x_{3}+\frac{1}{\sin ^{2} x_{3}}\right)\left(2 \sin ^{2} x_{4}+\frac{1}{\sin ^{2} x_{4}}\right)$$