Add the post type to the title of the page

You can try this:

/**
 * Modify the header title on single pages 
 * but exclude the 'post', 'attachment' and 'page' post types. 
 * 
 * Header Title:  Site Name | Post Type Label | Post Title
 *
 * Example:       My Shopping Site | Products | Sony Playstation 4
 */
function wpse_141145_wp_title( $title, $sep ) {

    if( is_single() && 'post' !== ( $pt = get_post_type() ) )
    {
        // Get the current post type object's 'singular name' else 'name':
        $pto        = get_post_type_object( $pt );
        $pto_lsn    = $pto->labels->singular_name;
        $pto_ln     = $pto->labels->name;
        $pto_title  = ( ! empty( $pto_lsn )  ) ) ? $pto_lsn : $pto_ln ;

        // Space around the separator:
        $sep = sprintf( ' %s ', trim( $sep ) );

        // Construct the breadcrumb:    
        $title  = get_bloginfo( 'name', 'display' );
        $title .= $sep;
        $title .= $pto_title;
        $title .= $sep;
        $title .= single_post_title( '', FALSE );
    }
    return esc_attr( $title );
}
add_filter( 'wp_title', 'wpse_141145_wp_title', 99, 2 );

where we modify the header title on single pages, but exclude the post post type.
We then recall that is_single() excludes the page and attachment post types.

Did you mean this kind of modification or did you have something else in mind?

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