How to set Last-Modified header from inside Loop

I’ve been trying to set the Last-Modified header from inside the loop, but I get a “headers already sent” error. I was using the_modified_date() and php’s header() function. I then tried setting the header in my functions.php file like this:

function modify_http_headers($headers)
{
	$headers['Last-Modified'] = date( 'c', the_modified_date() );

	return $headers;
}

add_filter('wp_headers', 'modify_http_headers');

But that doesn’t work because it’s not inside the loop so the_modified_date() doesn’t work. I searched Google for a long time and tried everything I saw. Can anyone help, please!