3. In a cube $A B C D-$ $A_{1} B_{1} C_{1} D_{1}$ with edge length 2, $M$ and $N$ are the midpoints of edges $B B_{1}$ and $B_{1} C_{1}$, respectively. If $P$ is a moving point in the plane $D M N$, when the distance from point $P$ to the plane $B C C_{1} B_{1}$ equals the length of $P D$, the eccentricity of the trajectory of point $P$ is $\qquad$
3. $\frac{2 \sqrt{34}}{17}$