Add the hidden fields to Wordpress' login, register, lost & retrieve password forms

hidden-login-form-field.php

function add_hidden_login_form_field() {
?>
  <input type="hidden" name="fromWPForm" value="<?php echo constant('LOGINFORMKEY'); ?>" />
<?php
}
add_action( 'login_form','add_hidden_login_form_field' );
add_action( 'lostpassword_form','add_hidden_login_form_field' );
add_action( 'retrievepassword_form','add_hidden_login_form_field' );
add_action( 'register_form','add_hidden_login_form_field' );