Delete song from iPhone and iTunes library simultaneously

What you want isn't possible with the way that iTunes syncing is designed. Sync lets you manage your content in the iTunes library, and then at some point update your devices to reflect the library. There is a certain facility for updating playlists and ratings in the other direction, but in essence syncing is iTunes to device, and only at connection time. If you want changes you make on the device to be reflected automatically in your iTunes library then subscribe to either iTunes Match or Apple Music to take advantage of iCloud Music Library. Hmm, come to think of it that still won't work if the tracks in your iTunes Library are downloaded to it. They will be removed from iCloud Music Library, but kept in the library and marked as removed in case you want to add them back later. However they wouldn't sync back to your device, nor would you need to connect it to iTunes physically to add or remove tracks.

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