4. Use a set of student's 

triangular rulers to form quadrilateral $A B C D$ as shown in Figure 3, where $\angle C B D=\angle C D B=$ $45^{\circ}, \angle B A D=2 \angle B D A$ $=60^{\circ}$, and let the angle formed by diagonal $C A$ and side $C B$ be $\theta$. Then $\tan \theta=$ $\qquad$
4. $\frac{\sqrt{3}-1}{2}$