I had another look at your code. You make the following replacement:
Cos[\[Theta]] Dt[\[Theta]] /. {\[Theta] -> \[Pi]/3}
Perhaps you expected theta to be replaced inside Cos[theta] alone. Unfortunately, it got replaced into Dt[theta] too, and Dt of a constant is zero. We must find a way to prevent this replacement. One way could be to first replace Dt[\[Theta]] -> inertSymbol, do your original replacements, and then convert back inertSymbol -> Dt[\[Theta]]. There must be a smarter way, but that's what comes to mind at the moment.
