DWV Assistance

[BradW]

Presently, I'm constructing a 1-1/2 story garage with an apartment on the 2nd floor and need some assistance on the DWV system. My problem is venting the W/C. When the foundation was poured a 3" main drain was stubbed out of the foundation wall directly below the W/C location on the second floor. The W/C is located in a 4 foot dormer with a window. My plan was to run 3-inch ABS from the stub out up to a 3x3x2 pick up the toilet flange and vent the W/C by running the 2 inch vent up into the stud bay and divert it around the window and out through the roof. The remainder of the DFU's (vanity/bath shower/washer box) on the second floor would tie together on a 2-inch drain and vent seperately from the W/C and tie into the vertical waste stack with a wye. My understanding was that the aggregate total of vents had to equal or exceed the main drain and somewhere I saw that the main vent stack had to be the same size as the main drain to atmosphere. After doing a little research I'm not sure this meets UPC on vent size requirements. Any enlightenment is appreciated. I attached a jpeg of plan if it helps any.

[pushkins]

Firstly I'd use PVC not ABS.
That dormer window does create a problem, ideally the 3" should run straight up and out (I'd love an ideal world...lol)
Do you have the room below the toilet (1st floor) to divert this stack to one side of the dormer ? I'm almost positive you need the 3" stack to exit the roof line 3"

Is that area behind the bath a chase ?, if so run the 3" up there.