I'm finishing the basement and have to add a bath tub as well as a toilet. My plan is to have a horizontal 3" tee, one side going to the toilet (about 16"), the second side to a 1 1/2" reducer which leads to the tub (about 24") and the third side ties directly into the main (vertical) 3" stack. Is that an agreeable solution? Do I need to vent the tub separately or can the main vent be used for the tub?