4. In Rt $\triangle A B C$, $\angle C=60^{\circ}$. A circle centered at $C$ with radius $B C$ intersects $A C$ at point $D$, and $B D$ is connected. Arc $\overparen{B D}$ and chord $B D$ divide $\triangle A B C$ into three parts (as shown in the figure). Then the ratio of the areas of these three parts $S_{1}: S_{2}: S_{3}=$ $\qquad$ .
Assume $B C=1$, then $S_{1}=\frac{\sqrt{3}}{2}-\frac{\pi}{6}, S_{2}=\frac{\pi}{6}-\frac{\sqrt{3}}{4}, S_{3}=\frac{\sqrt{3}}{4}$, so $S_{1}: S_{2}: S_{3}=(6 \sqrt{3}-2 \pi):(2 \pi-3 \sqrt{3}): 3 \sqrt{3}$.