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We need to free atleast 2GB so that Mac will bootup. Lets clear some old temporary system files from your Mac. Turn your Mac off. Turn it back on and immediately hold down the Command (Apple) key and the S keys at the same time. Then type the following command when it boot into black screen with white letters, hitting return after each commands. Make sure you enter them correctly and note the spaces between commands.
mount -uw /
rm -rf /Library/Caches/*
rm -rf /Users/*/Library/Caches/*
Hit return after entering reboot and then immediately hold down Shift key for 20 seconds. Then login to your account and delete some unwanted files, movies, musics etc and empty the Trash. Let me know if you get any errors when you run the commands.