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Copy Trans Manager is the i Tunes alternative that helps you add songs to your i Phone or i Pod without i Tunes.
But it is worth mentioning that this method is not secure to get your i Phone out of “Connect to i Tunes screen” status, because it may erase all data on your i Phone.
So, if any of your device is stuck on "Connect to i Tunes" screen then restart your device by using the following method.
If you are using i Phone 6 or earlier version then press and hold buttons together for about 10 seconds until the Apple logo appears on the screen.
i Phones could get stuck on "Connect to i Tunes" screen for various reasons and this can be really very destitute situation as you may not be able to access your i Phone anymore.
When this issue occurs, you won't be able to use your device and hence you will not be able to fix this issue.
This troubleshooting article explains how to fix the issue of i Tunes not syncing songs back to your i Phone or i Pod.