When comparing emails in the one click signin helper, use the existing utility

chrome/browser/ui/sync/one_click_signin_helper.cc

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "chrome/browser/ui/sync/one_click_signin_helper.h"
 
 #include <algorithm>
 #include <functional>
 #include <utility>
 #include <vector>
@@ skipping 1166 matching lines @@
         LogHistogramValue(source_, one_click_signin::HISTOGRAM_WITH_DEFAULTS);
       }
       OneClickSigninSyncStarter::StartSyncMode start_mode =
           source_ == SyncPromoUI::SOURCE_SETTINGS ?
               OneClickSigninSyncStarter::CONFIGURE_SYNC_FIRST :
               OneClickSigninSyncStarter::SYNC_WITH_DEFAULT_SETTINGS;
 
       std::string last_email =
           profile->GetPrefs()->GetString(prefs::kGoogleServicesLastUsername);
 
-      if (!last_email.empty() && last_email != email_) {
+      if (!last_email.empty() && !gaia::AreEmailsSame(last_email, email_)) {
         // If the new email address is different from the email address that
         // just signed in, show a confirmation dialog.
 
         // No need to display a second confirmation so pass false below.
         // TODO(atwilson): Move this into OneClickSigninSyncStarter.
         ConfirmEmailDialogDelegate::AskForConfirmation(
             contents,
             last_email,
             email_,
             base::Bind(
@@ skipping 65 matching lines @@
     contents->GetController().LoadURL(redirect_url_,
                                       content::Referrer(),
                                       content::PAGE_TRANSITION_AUTO_TOPLEVEL,
                                       std::string());
   }
 
   // Clear the redirect URL.
   redirect_url_ = GURL();
   sync_service->RemoveObserver(this);
 }