getenvironment() in Modules/_winapi.c needs to sort variables in the environment block and remove duplicates case insensitively [1]. 

The sort order used to matter with SetEnvironmentVairableW(). As soon as it reached a name in the environment block that compared greater than the target name, it would insert a new variable. Nowadays, SetEnvironmentVairableW() searches the entire environment block before inserting a new value. Regardless, at the very least, getenvironment() is not well-behaved and not setting the environment in the documented sort order that users, and possibly other programs, expect.

Case-insensitive sorting in Windows uses upper case. The variable names in the mapping can be added to a list and sorted with a key function that's based on LCMapStringEx() [2], with the flag LCMAP_UPPERCASE. Loop over the sorted list to create the environment block. Remove duplicates by skipping a name that compares equal to the previously stored name according to CompareStringOrdinal() [3].

_winapi.LCMapStringEx(src, flags=LCMAP_UPPERCASE, locale=LOCALE_NAME_INVARIANT) could also be used in ntpath.normcase(), which would resolve bpo-42658.

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[1] https://docs.microsoft.com/en-us/windows/win32/procthread/changing-environment-variables
[2] https://docs.microsoft.com/en-us/windows/win32/api/winnls/nf-winnls-lcmapstringex
[3] https://docs.microsoft.com/en-us/windows/win32/api/stringapiset/nf-stringapiset-comparestringordinal

I have a question, how to determine which name should be stored if they are duplicated with case insensitive?

> which name should be stored if they are duplicated with case insensitive?

Ideally os.environ would preserve the original case of the process environment, and os.environ.copy() would return a copy that's also case insensitive. That would prevent most problems with duplicates keys. See msg387676 in bpo-28824, and msg414319 in bpo-15373.

In msg390038 I suggested keeping the first key that's encountered. However, dicts preserve insertion order nowadays, so one could assume that the last one is the one that the caller wants to keep.