OLYMPIC-REVENGE 2019 Problem 1

Let $ABC$ be a scalene acute-angled triangle and $D$ be the point on its circumcircle such that $AD$ is a symmedian of triangle $ABC$ . Let $E$ be the reflection of $D$ about $BC$ , $C_0$ the reflection of $E$ about $AB$ and $B_0$ the reflection of $E$ about $AC$ . Prove that the lines $AD$ , $BB_0$ and $CC_0$ are concurrent if and only if $\angle BAC = 60^{\circ}.$