1. In $\triangle A B C$,
$$
\begin{array}{l}
z=\frac{\sqrt{65}}{5} \sin \frac{A+B}{2}+\mathrm{i} \cos \frac{A-B}{2}, \\
|z|=\frac{3 \sqrt{5}}{5} .
\end{array}
$$

Then the maximum value of $\angle C$ is