Sending UTF-8 emails from PHP to gmail, yahoo and outlook

<?
$headers  = "Content-Transfer-Encoding: 8bit\n";
$headers .= "Content-Type: text/html; charset=UTF-8\n";
$subject = 'Danish subject test æøå ÆØÅ.';
$body = "<!DOCTYPE HTML>\n<html>\nDanish subject test <b>æøå</b> ÆØÅ.\n</html>";
mail('[email protected]', "=?UTF-8?B?".base64_encode($subject)."?=", $body, $headers);
?>