When adding files to a database's filegroup. What is the procedure to
ensure all data is equally distributed across the newly added files (so
that everything is efficiently striped).

I have tried two things so far.
1) add a 3rd file, empty the main file, empty and drop the 3rd file
2) dbcc dbreindex every table in the database

both of these methods help spread the data but neither come close to an
even split. Is there a common best practice to use here?