3. $\frac{7}{8}$.

Connect $B D$ and $E C$ intersecting at point $O$. It is easy to see that $B D \perp E C$. Therefore, the angle $\angle B O D$ is the plane angle of the dihedral angle we are looking for.
$$
\begin{array}{l}
\text { In } \triangle B D O, \\
B D=2 \sqrt{2}, B O=\frac{8}{\sqrt{5}}, D O=\frac{2}{\sqrt{5}} . \\
\text { Hence } \cos \angle B O D=\frac{7}{8} .
\end{array}
$$
3. As shown in Figure 1, in rectangle $A B C D$, $A B=2, A D=$ 4, point $E$ is on line segment $A D$, and $A E=3$. Now, fold $\triangle A B E$ and $\triangle D C E$ along $B E$ and $C E$ respectively, so that point $D$ lands on line segment $A E$. At this moment, the cosine of the dihedral angle $D-E C-B$ is