Dutch Mathematical Olympiad

We have a triangle $△ABC$ and two points $D$ and $E$ on the line segment $BC$, such that $\angle BAD=\angle DAE=\angle EAC$. Furthermore, $|AB|=6$, $|BD|=4$, $|DE|=2$, and $|EA|=3$. See the picture on the right: be aware, it is not drawn to scale! What is the length of the line segment $CE$? A) 2 B) $2\frac{1}{4}$ C) $2\frac{1}{2}$ D) $2\frac{3}{4}$ E) 3