JBD,
I agree with you that there is only one phase angle for the current flowing in the wire.
To calculate the total current flow, you have to account for the phase angle differences in the summation.
I do agree with you that the result that you get by simply adding the single phase and three phase currents without considering phase angle will probably get you as close as calculating in the angles without knowing the power factor of the loads and thus the actual phase current angles.
-Jon
