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How to calibrate a camera with a movable camera?

Hi, I have a wide-angled camera and a home security camera which can be rotated vertically and horizontally by an API. My target is to move the second camera automatically to a specific position when I recognized something (e.g. a cat) in the first camera. That's why I have to calibrate both cameras.

I have found many examples of how to calibrate two cameras but none of them help me because my camera is moving... At the moment I have placed both cameras close to each other and stored the motor positions corresponding to the outer corners of the first camera. The target position is interpolated from this coordinates (which isn't so bad) but of course, this only works at a certain distance...

Does anyone have any idea how I can calibrate the two cameras?