Fitting a baseplate inside the camera screen at any angle?

This is how I want my game’s camera to behave, the camera focuses on the center of the baseplate, and only rotates around that baseplate

Given a FOV number and the ability to rotate at any angle around the X axis, i want to calculate the camera CFrame so that the baseplate will always fit inside the camera viewport

Accurate representation of this math problem here 1556546511292_30