Not sure why it had to be a video. I assume the lavatory trap is going to be a lot higher relative to the tub drain than you show it. Otherwise, on the surface, it appears to be okay. The vent connection can be any fitting you want, vent tee, inverted san tee, inverted combination Y-1/8 bend, or an inverted Y with an 1/8 bend. At that point it is immaterial.