10. Let $z_{1}, z_{2}$ be complex numbers, and $\left|z_{1}\right|=3,\left|z_{2}\right|=5,\left|z_{1}+z_{2}\right|=7$, then the value of $\arg \left(\frac{z_{2}}{z_{1}}\right)^{3}$ is
In $\triangle O Z_{1} Z$, $O Z_{1}=3, Z_{1} Z=O Z_{2}=5$, $O Z=7$. Applying the cosine rule, we get
$$
\begin{array}{l}
\cos \angle O Z_{1} Z=\frac{3^{2}+5^{2}-7^{2}}{2 \cdot 3 \cdot 5}=-\frac{1}{2} \Rightarrow \angle O Z_{1} Z=\frac{2 \pi}{3} \\
\Rightarrow \angle Z_{1} O Z_{2}=\frac{\pi}{3} \Rightarrow \arg \left(\frac{z_{2}}{z_{1}}\right)=\frac{\pi}{3} \text { or } \frac{5 \pi}{3} \\
\Rightarrow \arg \left(\frac{z_{2}}{z_{1}}\right)^{3}=\pi .
\end{array}
$$