Drain connections

I'd like to drain the overflow from an aquarium (self filling) to the waste water pipe in the basement. The most convenient place to access the pipe is the dishwasher connection from upstairs. There is a Wye in the main drain line, with a reducer and a threaded barb, which attaches to the DW upstairs. I was thinking I could put a Tee on this reducer and use that to hook up my aquarium.
I see several problems here, including possible backup of the dishwasher drain into the aquarium (dead fish) or back up sewer gas into the aquarium (dead fish). So what's the right way to do this?
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I would run the excess water to the garden....it should be good for the plants.....Ross
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