Do not tee into the drain. The proper way to add to the drain involves a double fixture fitting. It's a violation of plumbing code to "wet vent" a drain. If you were to "t" into the drain above the tee in the right-hand stud bay, that's wet venting, because you're dumping into the vent for the washer. If you tee into the drain below the tee, then the washer is wet-venting the vent for the sink.
The reason wet-venting is not allowed is under the right conditions, the flow of water from the wet-vented fixture can cause a vacuum in the drain line of the fixture below the wet-vent connection, which will **** the water out of the P-trap for that fixture. An empty P-trap is a path for sewer gasses to pass back into the structure.
Remember - plumbing drains are always "Air behind water"
One sweep to the left to accept the washer drain, one sweep from the right to accept the sink drain, and one up for the vent.
The sink and the washer should be able to share the same 1-1/2" vent line.
What you need looks like this:
http://www.accentshopping.com/product.asp?P_ID=152532
It's a larger fitting than the tee that's currently there. Get one that has 2" collars on the left, right and bottom, and a 1-1/2" collar in the middle. If you can only get 2x2x2x2, then get a 2" to 1-1/2" flush bushing for the middle top collar.
Other than that, tee into the water lines as previously noted, and you're good to go.