BALTIC-WAY 2000 Problem 4

Given a triangle $A B C$ with $\angle A=120^{\circ}$. The points $K$ and $L$ lie on the sides $A B$ and $A C$, respectively. Let $B K P$ and $C L Q$ be equilateral triangles constructed outside the triangle $A B C$. Prove that

$$|P Q| \geqslant \frac{\sqrt{3}}{2} \cdot(|A B|+|A C|) .$$