you can not win the case by simply repeating the things above to the judge, i guarantee you will lose.
here is the thing you can do, plea no contest or guilty, but ask for judge's leniency. usually the judge will give you a deal, which only requires you to pay the minimum find under the law.
if it's your first ticket, tell the judge you dont want your driving record to be ruined. judege may consider this and dismiss the case. in this case, you go free.
also you can search online, lot's of PDF file on sale can tell you how to plea not guilty and trick the cop.
but unfortunately, not always work.
hope this helps