SHARYGIN 2022 Problem 3

Let $CD$ be an altitude of right-angled triangle $ABC$ with $\angle C = 90$ . Regular triangles $AED$ and $CFD$ are such that $E$ lies on the same side from $AB$ as $C$ , and $F$ lies on the same side from $CD$ as $B$ . The line $EF$ meets $AC$ at $L$ . Prove that $FL = CL + LD$