Question: Help with 2D Numerical Integration

Hi,

     I'm trying to estimate a very diffcult integral with Maple. Here it is

restart;
chi:=Pi/2-theta:
epsilon:=0.001: 

Vsi:=-(1/sqrt( 1+epsilon - cos(chi)*cos(phi-Pi/3)) + 1/sqrt( 1 +epsilon- cos(chi)*cos(phi-Pi))+ 1/sqrt(1+epsilon-cos(chi)*cos(phi+Pi/3)));

evalf((Int(Vsi*SphericalY(3,2,theta,phi)*conjugate(SphericalY(2,1,theta,phi))*sin(theta), [theta=0..Pi,phi=0..2*Pi])));

I ultimatly want epsilon->0, but it causes 3 singularities, I think Maples can deal be able to deal with, but I left them out for now. 

Is there any particularly good method for an integral like this? Sphereical harmonics over the 2D sphere, with a possible singular potential. 

( I used 3,2, and 2,1, for the integral here. Some values it computes slowly, some it doesnt at all...)