Let  $L_1:x=y=z$
$L_2:x-1=y-2=z-3$  be two lines.
Let from origin O(0, 0, 0) on  $L_1$, perpendicular is drawn to $L_2$ has foot A. Segment OA is rotated about O by an angle ${90}^0$  such that  $L_2$ moves along with it, without changing its direction and becomes  $L_3$. A becomes B  $(\alpha ,\beta ,\gamma )$ then $\alpha +\beta +\gamma$ is equal to ____________