Integral over a surface

I am having problem with an integral. I dont know how to write in mathcode so excuse me for my notation.

This is in spherical coordinates:

x = theta
y = psi
r = radial component

the integrand is: (cos(x)/r^2)

I want to integrate this over a solid angle of an arbitrary surface.

da is a differential area. And in spherical coordiantes should be: da = r^2*sin(x)dxdy

I know the integral should be 4*pi but I dont get it right. I want to have the antiderivate as (cos(x)^2)/2 from 0 to pi.

Then I get 1/2*2pi = pi

So I am missing a factor 4 here. Can anyone help me show what I've missed?