Acrobatic single pilot reported a CFIT event during ATC assigned vectors. The pilot executed a 360 left turn due to ATC's lack of communication responsiveness to pilot's repeated calls for vector update.

Narrative

Enroute to ZZZ. Contacted Tower 12 miles out. No response. 11 miles out - no response. 8 miles out no response. 6 miles out - no response. I could hear Tower broadcast - but no response. I thought my radio might be inoperable and elected to continue to ZZZ as I had < 10 gallons fuel remaining. ZZZ Tower finally responded at about 4 miles out and then instructed me to enter an extended right downwind for Runway XX at about 3 miles out. 'I'll call your base'. Turned heading 080 for extended right downwind. After some time on this heading; it was apparent that I was headed into the side of a mountain to the North and East of ZZZ. There was about a 2000 ft. ceiling so I could not climb to avoid it. To avoid terrain collision; I executed a 360 degree left turn. Tower then lectured me that the turn was unauthorized. This was a potentially dangerous situation. Towers lack of responsiveness to my repeated calls created a problem where I had to make a decision to stay out of class C and riskpotential fuel depletion; or continue and be safe. Towers decision to keep me on 080 heading caused potential controlled flight into terrain. This could have been handled a lot better and more safely.