For the life of me I can't figure out how to draw up this part in solidworks:

What it is, is the interior part of an SMR (Spherical Mirror Retroreflector) I can get the sphere of the SMR, and the little black ring that goes around it but this golden part that sits in the center I have no idea how to make the cuts that would create three flat surfaces that converge at the center at whatever given angle. Any help would be greatly appreciated.

Here's another picture grabbed from google at a different angle:

I am not sure I understand the geometry perfectly, but this method might give you what you want.

Make a cylinder.

On the top sketch an equilateral triangle tangent to the cylinder.

Extrude cut thru all with draft for the angle you want.

Voila