4. In the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, the midpoints of edges $B B_{1}$ and $C C_{1}$ are $M$ and $N$, respectively. Find the angle formed by $A_{1} D$ and the plane $D_{1} M N$.
(Answer: $\arcsin \frac{\sqrt{10}}{5$.)