Hey Newtonian.

The first thing you need to do is find the distribution of A/B. Since A and B are going to be normal (since they are linear combinations of normals) then both A and B will be normally distributed as well. This link was provided on another forum in the discussion of ratios of normal variables:

http://www.jstatsoft.org/v16/i04/paper

In terms of your arctan function, you will then need to use a transformation theorem to get the PDF of arctan(B/A) and use the properties of the arctan function for getting the correct branch.