Add bounds to output from network

I basically have a simple CNN that outputs a single integer value at the end. This number is corresponding to a certain angle, so i know that the bounds have to be between 0 and 359. My intuition tells me that if i were to somehow limit the final value to this range instead of being unbounded like in most activation functions, i would reach any form of convergence sooner.

To try this, I changed the last layer and applied the sigmoid activation function, then added an additional lambda layer where i just multiplied the value by 359. However, this model still has a very high loss (using MSE, at times it’s actually greater than 3592 which is leading me to believe i’m not actually bounding the output between 0 and 359).

Is it a good idea to bound my output like this, and what would be the best way to implement it?