I installed a 100cfm fan in my main bath. I really do not want to vent through the roof. However, there are two sewer vents within five feet of the fan output. These sewer vents have 3" pvc which I could easily tee into. I would then put a rain cap on the vent so it would not ingest water down the bath fan vent ducting. Is there any reason I can't do this? My other option is a sidewall exhaust which would require a 28 foot run. I have a large attic above so space is not an issue.