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<!-- For the functions.php file in your theme: -->

function the_title_trim($title) {

  $title = attribute_escape($title);

  $findthese = array(
    '#Protected:#',
    '#Private:#'
  );

  $replacewith = array(
    '', // What to replace "Protected:" with
    '' // What to replace "Private:" with
  );

  $title = preg_replace($findthese, $replacewith, $title);
  return $title;
}
add_filter('the_title', 'the_title_trim');