Is 2 traps in same drain line ok?

I want to tie the plastic drain from a new additional shower into the drain of a bathtub 5 ft. away. The only easily accessable point is at the vertical tailpiece going down into the tub trap. If I have a trap at the shower too will this work?(would it work without the shower trap?) I assume I need a vent
beyond the shower trap.

Thanks for your advice.

No.

It's not okay.

There is a reason why each trap has a vent, and within certain dimensions.

The Shower drain should have a 2" trap and drain.

Most likely, the tub has been run in 1.5"

And you certainly wouldn't be allowed to run a shower and a tub into a 1.5" line.

Nothing is impossible,
Some things just take more time and money.

That's how most building inspectors and future homeowners would look at that.