Postprocessing (Integration) of a Far Field.

Dear colleagues,

SHORT QUESTION:
How to integrate Far Field emw.normEfar over the solid angle defined by inclination (polar) angle theta form 0 to 60 degrees, and azimuthal angle phi from 0 to 360 degrees?

IN DETAILS:
I am simulating a nano-antenna on the dielectric substrate, and managed to calculate the far field and the radiation pattern. In experiment the radiated from the antenna field will be collected by a lens with some numerical aperture. So, I need to calculate how much light is captured by objective, namely within the certain inclination angle, say 60 degree.

In other words I am looking for a way to calculate an integral of (emw.normEfar)^2 over the inclination (polar) angle theta form 0 to 60 degrees, and azimuthal angle phi from 0 to 360 degrees with radius equals to 1.

According to the equation view in the Far Field Domain the emw.normEfar is defined by sqrt(realdot(Efarx(x,y,z),Efarx(x,y,z))+realdot(Efary(x,y,z),Efary(x,y,z))+realdot(Efarz(x,y,z),Efarz(x,y,z))). Here I can replace the Cartesian coordinates with spherical: (x,y,z) -> (sin(phi)*cos(theta),sin(phi)*sin(theta),cos(phi)), and then take the double integral of the above function multiplied by r^2*sin(theta) over two angels.

QUESTIONS:
1) How to do a double integration? Which function to use?
2) Maybe someone knows the easier way to do the integration.

I would really thankful for any hints!
Maxim