3. As shown in Figure 1, in the regular triangular prism $A B C-A_{1} B_{1} C_{1}$, $D$ and $E$ are points on the side edges $B B_{1}$ and $C C_{1}$, respectively, with $E C=B C=2 B D$. Then the size of the dihedral angle formed by the section $A D E$ and the base $A B C$ is $\qquad$
3. $45^{\circ}$.

Let $B C=2$. Then the area of $\triangle A B C$ is $\sqrt{3}$.
Since $E C=B C=2 B D$, we have,
$$
\begin{array}{l}
E C=2, B D=1 \\
\Rightarrow A E=2 \sqrt{2}, A D=D E=\sqrt{5} \\
\Rightarrow S_{\triangle A D E}=\sqrt{6} \\
\Rightarrow \cos \theta=\frac{\sqrt{3}}{\sqrt{6}}=\frac{\sqrt{2}}{2} \Rightarrow \theta=45^{\circ} .
\end{array}
$$