Step 1: Bond angles in methane and trimethylamine.
The C–N–C bond angle in trimethylamine is very similar to the H–C–H bond angle in methane due to the sp\(^3\) hybridization of both carbon and nitrogen atoms.
Step 2: Conclusion.
Thus, the C–N–C bond angle in trimethylamine does not differ from the H–C–H bond angle in methane.