Integration over a portion of sphere

Questions
1

Hi,
I am trying to integrate a quantity

1/(Cos[theta] - Sin[theta]*Cos[phi])

over a spherical surface within the limits (theta, 0, ArcCot[Cos[phi]]) and (phi, 0, Pi/4). Due to some issue, which I am not able to figure out, not getting it done. Would be thankful if someone can help. Attached is the *.nb file with the code. Thanks in advance - SG

2

Your integral diverges at the limit of integration. When theta = ArcCot[Cos[phi]] then the denominator of the integrand is zero.

3

Thanks Jason, for pointing it out, though I was not expecting it. Will think over it, there is something wrong in my calculations.