CL-MO 2022 Problem 2

Let $ABC$ be a triangle such that $\angle CAB = 60^o$ . Consider $D, E$ points on sides $AC$ and $AB$ respectively such that $BD$ bisects angle $\angle ABC$ , $CE$ bisects angle $\angle BCA$ and let $I$ be the intersection of them. Prove that $|ID| =|IE|$ .