gdata: Remove use of FindEntryByPathSync() from RemoveEntryFromNonRootDirectory()

chrome/browser/chromeos/gdata/gdata_file_system.h

Index: chrome/browser/chromeos/gdata/gdata_file_system.h
diff --git a/chrome/browser/chromeos/gdata/gdata_file_system.h b/chrome/browser/chromeos/gdata/gdata_file_system.h
index 4e8dd920ea4e3044e5959bf36a7367cd8111ff83..be5f9acc4056f2242d94ae428ddc23a92147ae91 100644
--- a/chrome/browser/chromeos/gdata/gdata_file_system.h
+++ b/chrome/browser/chromeos/gdata/gdata_file_system.h
@@ -390,6 +390,12 @@ class GDataFileSystem : public GDataFileSystemInterface,
     const FileOperationCallback& callback,
     scoped_ptr<EntryInfoPairResult> result);
 
+  // Part of RemoveEntryFromNonRootDirectory(). Called after
+  // GetEntryInfoPairByPaths() is complete. |callback| must not be null.
+  void RemoveEntryFromNonRootDirectoryAfterEntryInfoPair(
+    const FileMoveCallback& callback,
+    scoped_ptr<EntryInfoPairResult> result);
+
   // Removes a file or directory at |file_path| from the current directory if
   // it's not in the root directory. This essentially moves an entry to the
   // root directory on the server side.