[Sync] Fix bug where DeviceInfo is missing a backup timestamp

chrome/browser/sync/profile_sync_service.h

Index: chrome/browser/sync/profile_sync_service.h
diff --git a/chrome/browser/sync/profile_sync_service.h b/chrome/browser/sync/profile_sync_service.h
index 5393c5f6b16babc050182f7d00972df1b4430ac1..a8bcc3c3cd035646d78e764475d4c2f3ea1ea21a 100644
--- a/chrome/browser/sync/profile_sync_service.h
+++ b/chrome/browser/sync/profile_sync_service.h
@@ -987,10 +987,6 @@ class ProfileSyncService : public ProfileSyncServiceBase,
   // This specifies where to find the sync server.
   const GURL sync_service_url_;
 
-  // The last time we detected a successful transition from SYNCING state.
-  // Our backend notifies us whenever we should take a new snapshot.
-  base::Time last_synced_time_;
-
   // The time that OnConfigureStart is called. This member is zero if
   // OnConfigureStart has not yet been called, and is reset to zero once
   // OnConfigureDone is called.