Installing Clawfoot tub in roughed in bathroom

Hi folks. I'm finishing our master bathroom that was never completed. It was roughed in. My question is if a vent is needed. The bathroom has a toilet (vented), sink(vented), shower (vented), and tub which drains and seems to be wet vented to the sink. The sink is 2 inch pipe and the tub branch is 1.5 inch. I am limited to working within the floor joists so I don't know how adding a vent will work within those confines since everything must be under subfloor (clawfoot visibility). Be advised the bathroom is drywalled and the home has been finished since 1998. These photos were taken from a video done by the original owner during construction. We will not install a stand alone shower and will utilize the clawfoot as a shower occasionally. Is this wet vent adequate?

How far is it from the P-Trap to the drain line?
I would assume that you will not have any issues using a 2 inch drain line as a wet vent.

Again, should be fine..
Michael

It is 16 inches from the end of the p trap to a 90 elbow, and 50 inches from that elbow to the 2 inch drain line. Total of 66 inches.