Designing rear projection installations using mirrors is not as complicated as it may seem, once the basic principles are understood.
Make a drawing in scale of a side view of the screen, projector and the projection cone. Cutting it out will enable you to fold the light path or projection cone,
simulating the configuration of the mirror system.
The folds in the paper represent a mirror and this method will allow a reasonably accurate calculation of built-in depth and mirror sizes.