My question involves a traffic ticket from the state of: North Carolina

I was driving down the highway going my normal speed of 4-6 over the speed limit. The time was roughly 1:30 am and there was pretty much no traffic on the highway. A car with its brights came up behind me and tailgated me a solid 2 minutes when I was in the left lane. I then turned into the right lane of the highway and this car continued to tailgate me with his or her brights for another minute. We were coming up to a semi truck and the car was proceeding to go into the left lane. I turned my brights and shifted into the left lane. The car accelerated and continued to accelerate to a speed beyond what I was willing to follow anymore.

I quit pursuing the vehicle when I hit the speed of 77 mph in a 65. The car continued to pull away. I was roughly about 70 car lengths away from this vehicle, then it suddenly braked. I was a good distance away so I shifted into the left lane as I was decelerating without braking back to my normal speed of 69-71 mph for a 65. The car which was very much ahead of me continued to slow itself as I then passed them and then they maintained a speed of 67-70 mph. I continued to drive for about half a minute before another car came up behind me and then the blue lights came on.

The other car was the same color as my car and looked very much like my car from the back, it was very dark out and I literally think that the state trooper got our 2 vehicles mixed up because I am almost 90% sure that I never broke the speed of 79 mph. as I never passed nor did I gain on the lead vehicle. Until that vehicle braked heavily and I was already decelerating.

The officer said I was going fast and asked me what speed I thought I was going I told him 77 mph. He replied "I clocked you at 82." I was shocked.
I told him that my Gps and my Speedometer couldn't both be off because I would have noticed going over 80. He told me to get my speedometer recalibrate and to fax it to the office.

I am innocent and this is a big mix up. Considering that the other car was swerving, speeding, and driving recklessly. I managed to get their ticket.
What should I do?