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add_action('template_redirect', 'sp_add_last_modified_header');
function sp_add_last_modified_header($headers) {
  //Check if we are in a single post of any type (archive pages has not modified date)
  if( is_singular() ) {
    $post_id = get_queried_object_id();
    if( $post_id ) {
      header("Last-Modified: " . get_the_modified_time("D, d M Y H:i:s", $post_id) );
    }
  }
}