Navigation on a tidally locked planet

I have a tidally locked planet on a circular orbit, with an axial tilt of 22.5Â° That means one side is always in the sun, the other one in the shade. The subsolar point moves along a north-south line during each rotation around the sun, 22.5Â° each way. The night side can see the stars.

How would someone on this planet determine their position? Both on the night and the day side? What tools would be necessary? Sextant, some sort of table of celestial positions, a time-keeping device? How precise would it have to be?

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Navigation on a tidally locked planet

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