Q: my iPhone won't now sync with my mac despite installing and updating all latest versions of operating system and iTunes.  I only attempted to restore settings as my phone was unable to connect to phone provider (all other apps, wifi etc, were working)

Hello Magmaga,

It sounds like you are trying to use iTunes to restore your phone but keep getting error code 3. I recommend these steps for that error message from the article named:

Resolve specific iTunes update and restore errors

http://support.apple.com/kb/ts3694#3

Check for hardware issues

Related errors: 1, 3, 10-47, 1002, 1011, 1012, 1014, 1000-1020, 1669.

Try to restore your iOS device two more times while connected with a cable, computer, and network you know are good. Also, confirm your security software and settings are allowing communication between your device and update servers. If you still see the error message when you update or restore, contact Apple support.

Thank you for using Apple Support Communities.

All the very best,

Sterling