sync: remove GetAuthenticatedUsername from ProfileSyncService/SyncBackendHost.

chrome/browser/sync/internal_api/sync_manager.h

Index: chrome/browser/sync/internal_api/sync_manager.h
diff --git a/chrome/browser/sync/internal_api/sync_manager.h b/chrome/browser/sync/internal_api/sync_manager.h
index eaf5ccb1fe89b0b6f9c2e5a5f8125512dffe2368..5daed18e3a651202e65fbb087707c1d883cf309e 100644
--- a/chrome/browser/sync/internal_api/sync_manager.h
+++ b/chrome/browser/sync/internal_api/sync_manager.h
@@ -443,11 +443,6 @@ class SyncManager {
   // Checks if the sync server is reachable.
   void CheckServerReachable();
 
-  // Returns the username last used for a successful authentication.
-  // Returns empty if there is no such username.  May be called on any
-  // thread.
-  const std::string& GetAuthenticatedUsername();
-
   // Check if the database has been populated with a full "initial" download of
   // sync items for each data type currently present in the routing info.
   // Prerequisite for calling this is that OnInitializationComplete has been