We have a powder room on the main floor with a toilet that has a sluggish flush. It's not clogged. While investigating the issue I discovered that neither the toilet nor sink in the powder room is vented (the full bathroom on the second floor is vented).
When I remove the powder room's sink from its waste pipe, and attempt to use that as an air vent for the toilet, the toilet flushes perfectly.
What are some permanent fixes to this problem?