Given a 3D camera and a horizontal plane both at the origin, how can I determine the pitch of the camera to view the plane N units below the horizon?

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Given a 480px x 480px screen, and a 3D camera at the origin, with a horizontal plane on the X-Z axis that cuts through it (seen as a horizontal line through the center of the screen), how can I determine the pitch rotation necessary to see this plane any number of pixels below the middle horizon where it originally was?