Can't change iCloud ID
I've a problem:
I've changed my apple ID a week ago in ios 6. Everything was working fine until I've updated to ios 7 today. In ios 7 I've to re-enter my iCloud id password. That's not a problem but the password isn't accepted. This is because the iCloud ID is still configured to use my old apple ID! It's greyed out, so I can not change it. The solutions that I've found all telling to delete the iCloud ID first and then to connect it again with the new credentials...., but in Ios 7 there is a new security feature: To delete the iCloud ID you've to first logon to disable find my iPhone! I can't logon beause of the wrong id :-( the chicken and the egg....
Please apple help!
iPhone 5, iOS 7