I try to activate xamarin account on Visual Studo 2015 Update 2 the error is:
System.FormatException: One of the identified items was in an invalid format.
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Updating Xamarin to the latest stable version worked for me.
If you still having issues, goto Tool Menu , then Options, Under Xamarin, choose Other and then click on Check Update button, You should find an update pending ( 4.0.3.214), download that and try again. It should work.
Take a look at this discussion in the Xamarin forums. There are listed several common issues. Your question's there as well:
Xamarin for All! Stable Release: Xamarin 4, Cycle 6 – Service Release 3
Quoted from there:
Ensure that you have updated all of your installed Xamarin packages on both Windows and Mac to match the versions listed under "Release Info" below.