Accidentally removed an authorised device from itunes

Question

Under iTunes
Use Store > View My Account
Under iTunes in the Cloud click Manage Devices. I accidentally removed the wrong iphone as an authorised device. How do I re-authorise it?
iTunes will no longer recognise that the device is plugged in to my Windows 8 laptop.

Answer 1

The last time I seriously had an issue with iTunes was several
versions ago, and I had to find and remove several files other
than just the iTunes application in order to reinstall an all new
(or All-Old) installation; so none of the former items were inside
the computer. And that's been so long ago, I am uncertain now
what items, hidden in several folders, need to be tossed out.
{There are Packages, such as iTunes Access, iTunes X, iTunes,
etc in the system; there may be plists (preferences) or other
related stuff. Almost a mystery in where the right ones hide out.}
You should not have to worry about the iTunes music library,
since it can be left where it belongs unless you are reverting
to an iTunes player that can't support some new codec or
compression, or other technologies.
But since you aren't going back to an earlier version, you
only have to remove the section of the installed iTunes
that is not the Application itself; perhaps a preference plist
or Application support file has some iTunes parts, to toss.
The replacement item to that you accidentally lost would
not be reinstalled unless the computer sees it has No iTunes
files of the type that radio station (and others) existed in.
So, tossing & emptying Trash won't get rid of these other files.
That's where the necessity to know where to go comes in.
And like I said, it has been several versions ago, when I had
to remove all iTunes support files (except music library) and
reinstall - then, it was to revert to a version one number older.
That's the direction to take, though. Try a search for 'reverting
iTunes' in google to see what kinds of articles show up.
PS: There are a few uninstaller utilities for Mac OS X that
may be able to help find & remove all the items iTunes in-
stalled in the first place; of course, I can't recall the names.
It's only 2AM here.
Good luck & happy computing!
{ edited }