The tub's vent must be downstream of it's trap. The sink would need it's own vent to prevent it's trap from siphoning. The low heel inlet mounted horizontally is strictly prohibited in most places.
A proper connection on the same level would require a wye downstream of the water closet (if there was room), or a side inlet tee installed in the vertical stack.
Knowing where you are or what plumbing code you fall under can be a determining factor as to what is allowed or not allowed.