I just started learning Mathematica Kindly help me with this code. My actual Expression is about 300 lines in which I have many ArcTan[exp1,exp2] forms, a solution to the toy problem which framed bellow might help me to solve my actual code issues.

I have a function

f[x1_, x2_] := 
  Cos[x2*ArcTan[x1, x2]] + 
   Sin[x1*ArcTan[x2, x1] + 
      ArcTan[x1^2, x2]]*
    E^ArcTan[x1 + x2, x1] 

For some values of x1 and x2 I will have ArcTan[0,0] form inside f[x1,x2]. My aim is to replace ArcTan[0,0] with a value "a".

What I did is

f[x1_, x2_] := 
  Cos[x2*ArcTan[x1, x2]] + 
   Sin[x1*ArcTan[x2, x1] + 
      ArcTan[x1^2, x2]]*
    E^ArcTan[x1 + x2, x1]

ReleaseHold[f[0, 0] /. ArcTan[0, 0] -> 0]

This is not working

I even tried this

f[x1_, x2_] := 
  Cos[x2*ArcTan[x1, x2]] + 
    Sin[x1*ArcTan[x2, x1] + 
      ArcTan[x1^2, x2]] /. 
   ArcTan[0, 0] -> 0

f[0, 0]

This is not working.
Kindly suggest me a way.