The camera needs to have the same field of view as the angle of the spot light. Which turned out to be tricky to adjust because the camera setting only accepts values for the focal length.
But fortunately Casual reveals in an archive thread the relation between focal length and field of view for a Carrara camera: http://forumarchive.daz3d.com/viewtopic.php?t=175284
The formula finally collapses to: Focal Length = (21,677 / (tan (Spot Angle / 2))
So a spot angle of 140° would correspond to a focal length of 7,9 mm.
The render output must be quadratic. I disabled visibility of everything but the mirror and rendered with a white background. For using the render directly, the Invert Color box must be ticked in the spot’s Gel adjustments.