Dear community, I am trying to manipulate algebraic expressions for the propagation of tidal waves. In particular I would like to expand the trigonometric functions. If I do that as follows, I obtain the expected result.

TrigExpand[Cos[a + b] + Cos[c + d]]
Cos[a] Cos[b] + Cos[c] Cos[d] - Sin[a] Sin[b] - Sin[c] Sin[d]

However, if I try something like

TrigExpand[ArcTan[Cos[a + b] + Cos[c + d]]]    
ArcTan[Cos[a + b] + Cos[c + d]]

Mathematica does not seem to recognize it has to expand the trigonometric functions that are in the Argument of ArcTan. How can I force Mathematica to return

ArcTan[Cos[a] Cos[b] + Cos[c] Cos[d] - Sin[a] Sin[b] - Sin[c] Sin[d]]