[sync] Clean up path generation for the local sync database.

components/browser_sync/profile_sync_service.h

Index: components/browser_sync/profile_sync_service.h
diff --git a/components/browser_sync/profile_sync_service.h b/components/browser_sync/profile_sync_service.h
index ee7fa2f9e7d73680d692b5f2188feb659dd10acf..7048a483f899c0dd998749f02a638d8fbc3049eb 100644
--- a/components/browser_sync/profile_sync_service.h
+++ b/components/browser_sync/profile_sync_service.h
@@ -241,7 +241,6 @@ class ProfileSyncService : public syncer::SyncServiceBase,
     std::string debug_identifier;
     version_info::Channel channel = version_info::Channel::UNKNOWN;
     scoped_refptr<base::SequencedTaskRunner> blocking_task_runner;
-    base::FilePath local_sync_backend_folder;
 
    private:
     DISALLOW_COPY_AND_ASSIGN(InitParams);
@@ -786,9 +785,6 @@ class ProfileSyncService : public syncer::SyncServiceBase,
   // engine to refresh its credentials.
   bool is_auth_in_progress_;
 
-  // The location where the local sync backend stores its data.
-  base::FilePath local_sync_backend_folder_;
-
   // Information describing an unrecoverable error.
   UnrecoverableErrorReason unrecoverable_error_reason_;
   std::string unrecoverable_error_message_;