Air carrier Captain reported an unstabilized approach while maneuvering at night in visual conditions. During the maneuver the Captain determined they could not maintain terrain clearance; initiated a climb; and was provided vectors by ATC and landed on the opposite runway.

Narrative

Because of weather and airspace changes we were high enough at 4 miles from the FAF to ask Tower for a left 360 at 4200 feet in VMC at night. There was no way we would make the decent to runway 11 and be stable. We asked for and received clearance for a left 360 from Tower. We started a left 360 while still descending and I verbally stated that the MSA was 6000 as we were handed back off to Approach Control by Tower. They informed us that they couldn't give us terrain clearance and said continue at our own risk.I immediately disconnected the autopilot and started a right turn back toward the final while initiating a climb when I realized our terrain clearance wouldn't be enough for the 360. I then told the FO to ask for a heading and altitude. We then established the aircraft back on a safe path away from the terrain. ATC asked if we could land the opposite runway; 29; and we agreed with calm winds and set up for the approach and landing.No other issues occurred and we landed without incident.