8. In $\triangle A B C$, $\angle B=\angle C=30^{\circ}, B C=2 \sqrt{3}, P, Q$ are on line segments $A B$ and $A C$ respectively, $A P=1, A Q=\sqrt{2}$, line $A D \perp B C$ at $D$. Now, fold $\triangle A B C$ along $A D$, when the dihedral angle between plane $A D B$ and plane $A D C$ is $60^{\circ}$, the length of line segment $P Q$ is $\qquad$ .
Given, $A B=A C=2, A D \perp B C \Rightarrow \angle B D C=60^{\circ}$ $\Rightarrow B C=\sqrt{3}$, in $\triangle A B C$, $\cos \angle B A C=\frac{4+4-3}{2 \cdot 2 \cdot 2}=\frac{5}{8}$, so in $\triangle A P Q$, $P Q^{2}=1+2-2 \sqrt{2} \cdot \frac{5}{8}=\frac{12-5 \sqrt{2}}{4}$ $\Rightarrow P Q=\frac{\sqrt{12-5 \sqrt{2}}}{2}$.