Recently i was driving around town( a very small one, the population is about 2000) and was going down a familiar road i usually take to get home, when I saw a police car getting ready to turn in the same road i was currently traveling in. I clearly saw the officer turn and proceed behind me so i checked the speedometer and i was in the clear and then some.The officer was a good 1000 feet behind me and i just kept my cool like anyone does .
The officer then proceeded to follow me turning in at every turn i usually take to get home right behind me. He then turned into the street i live on and followed me to the last stop sign right before my house. This is when i was sure i was going to get pulled over, as soon as I was speeding up after the last stop sign I saw the lights go up. I pulled over a few steps from my house and waited for the officer to approach my vehicle.( I had gotten a ticket about 4 months prior to this event and my dad was not going to like this, so i was feeling horrible.)
So the officer comes and looks me in the face and as soon as he does he smirks and says "that was some nice driving you were doing back there" in a taunting voice. He looked innocent enough until he saw ME behind the wheel then his face took a "I got this chump" direction. I had never seen this officer in my life and I was a bit surprised at the way he spoke to me. I was going to defend myself because i wasn't speeding and that i was completely sure of, but it was me vs the cop and he (obviously) was going to be right no matter what. He continued to talk to me as if making fun of me and stating false facts." I was going 40 trying to catch up to you" when the speed limit was 25.
He didn't get me with the speed radar they use so i was just dumbfounded as to how this could possibly be happening (i was being falsely accused for what i knew was no reason at all.) Obviously the officer was going to have to speed up to catch up to me i was pretty far distance from him to begin with, and i couldn't believe his stupidity. In the frustration of another sure ticket I put my left arm down on my left leg trying to calm myself and just ease up. The officer pulled his gun out and asked me what i was doing.(yes, it was crystal clear i put my hand on my left leg, there were no sudden or sneaky movements, just one single smooth normal motion.)With the gun out he told me to put my hands up on the steering wheel because it was better for me, and I did.
It was at this moment that reinforcements arrived and i was starting to look like a problem to my neighborhood, the second officer placed himself directly outside my door with his hands on his gun which didn't help. The officer which stopped me in the first place then went to his vehicle and did what all cops do when they give you a ticket, stayed there for about 5 minutes. He then called me out of the car towards his car where he told me why i was getting a ticket. He told his partner he was going 45 MPH trying to catch up to me which then left me without any doubt that he was lying. (He earlier stated to me that i was going 40 MPH on a 25 MPH zone.)
The ticket was for speeding but he said that he should have given me a ticket for reckless driving which i was doing, according to him.He said i could pay the ticket or go to court and fight it, but when he said i could fit it he said it in a snickering voice and he said that fighting it was risky. I got my ticket and walked back to my car, then i looked back and saw both of them laughing for some reason sitting on the hood of a police car. This also led me to think that it was just some kind of joke to them while to me it was a 200$ dollar loss.

Now, the next morning i went to the courthouse and got a court date which is in about 4 days and i want to know if i have a chance at winning this case.There is no evidence of anything done wrong at all, no radar, and the officer kept fumbling speed limits, so he wasn't even sure what to say.
If possible that there was a recording device on his vehicle it would show how he was getting speed limits out of the blue.I have never had anything against cops because i don't see them as enemies but as protectors but this... this is in no way protecting anyone.

So what i have is a 200$ ticket, 3 points on my license on my hands and a court date in 4 days and I have no clue if i have a chance to win this or not and just wanted a little advice or any suggestions on what i can do because its basically my word against the officers'.