It appears that you are aiming to display a specific point on your sphere (possibly with an earth texture) on Google Maps, which necessitates having the latitude and longitude coordinates. Using 2D screen coordinates for this purpose strikes me as an unconventional approach.
Presumably, your camera is positioned around the sphere at the center of the coordinate system. To obtain the latitude and longitude information, I would recommend converting the camera position to polar or spherical coordinates, focusing on angles rather than radius. By following this method, you can easily derive the desired latitudinal and longitudinal values.
https://i.sstatic.net/7pHUt.jpg
To convert from your camera’s Cartesian coordinates (x, y, z), you can refer to this handy resource: Conversion between Spherical and Cartesian Coordinates Systems
https://i.sstatic.net/uypzI.png
https://i.sstatic.net/PEPle.png
It’s important to note that in the formulas and graphical representations, you should interchange the y and z values if working in three.js, where y represents the upward direction (and potentially requiring z inversion).
Next, you’ll need to translate phi (ranging from 0 to 2*PI) and theta (from 0 to PI) into longitude (-180° to 180°) and latitude (-90° to 90°), a relatively straightforward task.
Your sphere’s prime meridian should align with the positive x-axis.
(Feel free to correct any mistakes in my explanation.)