Adding shower to Laundry Trap

I have a laundry room on the first floor of our slab style two story home. I would like to add a shower drain to this 3" pipe. I understand that it will have to be with a 2" pipe and a rise of 1/8" to every foot.
Now for the question:
If I put the shower on a platform and tee off of the washer drain pipe after the trap, do I have to add another trap on the drain to the show also?

The goal is 1/4" per foot for slope on a drain line (you can get by with less on larger pipe). Yes, the shower needs it own trap AND vent. Putting a shower up on a platform to get the required slope always looks funky, and, depending on the house, can really crowd the height.