7. In the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, points $\mathrm{M}$ and $\mathrm{N}$ are on segments $A B$ and $B B_{1}$ (excluding the endpoints of the segments), respectively, satisfying $A M=B_{1} N$. Then the range of the angle formed by $A_{1} M$ and $C_{1} N$ is $\qquad$
7. $\left(0, \frac{\pi}{3}\right)$
$$
=\frac{\left(A_{1} A+A M\right) \cdot\left(C_{\left.C_{1} B_{1}+B_{1} N\right)}^{\operatorname{und}}\right)}{\sqrt{\left(x^{2}+a^{2}\right) \cdot\left(x^{2}+a^{2}\right)}}=\frac{\operatorname{urr}_{1} A \cdot B_{1} N}{x^{2}+a^{2}}=\frac{a x}{x^{2}+a^{2}}=\frac{1}{\frac{x}{a}+\frac{a}{x}} \in\left(0, \frac{1}{2}\right) \text {, so } \theta \in\left(0, \frac{\pi}{3}\right)
$$