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`AccountManagerUI` is used by `AccountManagerFacadeAsh` to show system
UI (system dialogs, OS Settings etc.). `AccountManagerFacadeAsh` cannot
show system dialogs directly because it is inside
chromeos/components/ and can not depend on chrome/browser/.

`InlineLoginDialogChromeOS::Show` methods will be private, so no one can
call them directly. These methods will be called only by
`AccountManagerUIImpl`. Also, `InlineLoginDialogChromeOS` will not send
UMA stats anymore (they will be sent by `AccountManagerFacade` instead).

Bug: 1140469
Change-Id: I5f204d2dfcae7e8c920af672f1d4d7109ae1c5f7
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2550741
Commit-Queue: Anastasiia N <anastasiian@chromium.org>
Reviewed-by: Kush Sinha <sinhak@chromium.org>
Cr-Commit-Position: refs/heads/master@{#835637}