tapping into existing drain for new sink

Our rec room has a stub-in for water lines in the subfloor and we would like to put in a wet bar. In the crawl space immediately adjacent to the water lines there is a drain line coming from the sinks in the upstairs bathroom. Can I tap into the existing drainline (at a 45 angle?) for the new sink drain to be installed? Or is this inadequate venting?

sink

It would be inadequate venting, and you cannot cut into the line without providing a vent, and especially not at a 45 degree angle.