Catera Cooling System

Just bought a 2000 Catera with 52,000 miles. Car is perfect except it is losing about 3/4-gallon of coolant per week. There are no leaks. The oil looks clean with no sign of anti-freeze contsmination. There is no white smoke from the tailpipe

Are you sure there are no leaks, or is the radiator cap weak and allowing steam to escape as you’re driving and might not notice it?