4. In an acute triangle $ABC$, $\angle A=30^{\circ}$. A circle is drawn with $BC$ as its diameter, intersecting $AB$ and $AC$ at points $D$ and $E$ respectively. Connecting $D$ and $E$, the triangle $ABC$ is divided into triangle $ADE$ and quadrilateral $BDEC$. Let the areas of these shapes be $S_{1}$ and $S_{2}$ respectively, then $S_{1}: S_{2}=$ $\qquad$ .