Let $ABC$ be an equilateral triangle. For an arbitrary line $\ell$. through $B$, the orthogonal projections of $A$ and $C$ on $\ell$ are denoted by $D$ and $E$ respectively. If $D\ne E$, equilateral triangles $DEP$ and $DET$ are constructed on different sides of $\ell$. Find the loci of $P$ and $T$.