php - How to automatically detect user's timezone? - Stack Overflow
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Or use current_timestamp() in last_login, then set session_expiry in sessions table to current_timestamp + 3600. Now I remember what I was thinking yesterday!
StackOverflow is a great website that gives you a lot of help with your projects. You just need to learn which questions are right and which are wrong. And regarding your code, I think it's clear and understandable. Not "fat".