simple wp_title filter

Hey guys I’ve made a page that shows different content depending on a variable on the URL, but my problem is I’m trying to find a way to make it so that the page will change title as well depending on what’s showing, so I had this made but is not working

add_filter( ‘wp_title’, $page_title, 10, 2);

I just need something simple like that and I will automatically change the $page_title variable any ideas of what I’m doing wrong, or maybe there’s a different way, or is there a way to use shortcode on a page title?

thanks