Tying laundry tub to cleanout
 

I want to put a laundry tub in my basement.
I have a clean-out in the floor about 10 feet from the waste stack.
My idea is to tie the laundry tub drain line into the the clean-out.

I have a couple of questions before I move forward with my plan -

1. Would I need to run a vent line for the laundry tub?
2. Should I be concerned about sewer gas backing up into the
basement, via the laundry tub drain?
3. I have a washing machine already installed in the basement,
will I need to worry about the laundry tub getting backed up with
the washer discharge?

I did consider tying the laundry tub into the the wash drain,
but the washer drain is about 4 feet from the floor.

Thanks -

Dave