How can I prove that I wasn't at fault in a car accident I was ticketed for?

Long story short - in an accident. I was driving my car along the route I take 4 days a week, there fore I am well aware of how the lights work. Weather conditions were fine. I stop at one intersection's red light. Up ahead, about 8-10 cars lengths, is the next set of lights. When my set of lights changed green I proceeded. It's a 50km zone and I am aware of this as well. After ping the intersection I swicthed to my left lane. Now, every time I've ever driven thru here during peak hours (9am this day) once that 1st set of lights I stopped at turns green, the next set turns green not even 30 seconds later. I ume to keep the flow of traffic as it would get quite congested otherwise. This day though, I noticed a large transfer truck make a wide right turn from this intersection, and then out of no where was the truck I ended up t-boning. I got the ticket for failing to yeild to a traffic signal. I dont think it was my fault tho. How can I prove the lights would have been green?