Each Android device usually comes with its own custom camera application made by the manufacturer of that device. Each of them has its own interface and, probably, its own path / place for storing this parameter, if it exists even for this device. Therefore, any answer to this question will be highly device dependent.
But even if you simply limit yourself to the AOSP camera application, which is the application used on Nexus devices, there is no API for this. The application will ask if you want to enable the GPS tag when you first start the application, after which you can find the option to enable / disable geotags in the settings.
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