The above equation should describe the resulting plane you’ll get if you start with a plane lying in the XY plane, then rotate it 45 degrees CCW around the X axis, then rotate it 30 degrees CCW around the Y axis.

Is it easier to do it that way in Solidworks? If so, how is that done?

Relabel the standard planes to minimize confusion later. Front is XY, Top is XZ, Right is YZ.

On the XY plane, sketch a circle with radius 1 centered at the origin.

Extrude this sketch along Z from the midplane to your specified extents.

Sketch a construction line on one of the standard planes; this will be the projection of your plane equation onto this plane. I used the XY plane. I imposed dimensions on this line (delta_x = 1, delta_y = .5) but you could make the line driven by a forumula instead if you desired.

Repeat the previous step on another of the standard planes. I used the XZ plane. delta_x = 1, delta_z = -1/sqrt(3).

Add a reference plane that is coincident to both of the construction lines drawn in the previous two steps.

Cut a section through the body at the reference plane.