NL-NWO 1968 Problem 4

Given is a triangle $ABC$ . A line $\ell$ passes through reflection wrt $BC$ changes into the line $\ell'$ , $\ell'$ changes into $\ell''$ through reflection wrt $AC$ and $\ell''$ through reflection wrt $AB$ changes into $\ell'''$ . Construct the line $\ell$ given that $\ell'''$ coincides with $\ell$ .