Should 3 takeoffs and landings to stay day current be solo?
Yes you can count that time as PIC and towards this currency requirement.

The regulation requires that you are the only one who moved the flight controls during takeoff and landing. This means you could fly with anyone else in the cockpit (including a flight instructor, another pilot, or non-pilot friends) but you alone must be the person who performs those takeoffs and landings in order to remain qualified.

This eliminates a few scenarios from counting towards the currency requirement, including:


You flew with another pilot, counted yourself as PIC (because you were more qualified or by prior arrangement) but didn’t actually do the work yourself
You flew with an instructor, and they helped you with the landings