There are many ways to skin a cat when it comes to implementing wp_title() - http://ziadrahhal.com/2012/05/recommended-wp_title-filter-in-wordpress

WordPress Title Filter A

        // http://ziadrahhal.com/2012/05/recommended-wp_title-filter-in-wordpress
        // http://codex.wordpress.org/Plugin_API/Filter_Reference/wp_title
        // http://codex.wordpress.org/Function_Reference/wp_title

        // Title tag filter
        // required for themes
        // a custom callback function that displays a meaningful title
        // depending on the page being rendered
        function wp_flex_title_filter( $title, $sep, $sep_location ) {

            // add white space around $sep
            $sep = ' ' . $sep . ' ';

            $site_description = get_bloginfo( 'description' );

            if ( $site_description && ( is_home() || is_front_page() ) )
                $custom = $sep . $site_description;
            elseif( is_category() )
                $custom = $sep . 'Category';
            elseif( is_tag() )
                $custom = $sep . 'Tag';
            elseif( is_author() )
                $custom = $sep . 'Author';
            elseif( is_year() || is_month() || is_day() )
                $custom = $sep . 'Archives';
            else
                $custom = '';

            // get the page number (main page or an archive)
            if( get_query_var( 'paged' ) )
                $page_number = $sep . 'Page' . get_query_var( 'paged' );

            // get the page number (post with multipages)
            elseif( get_query_var( 'page' ) )
                $page_number = $sep . 'Page' . get_query_var( 'page' );
            else
                $page_number = '';

            // Comment the 4 lines of code below and see how odd the title format becomes
            if( $sep_location == 'right' && !( is_home() || is_front_page() ) ) {
                $custom = $custom . $sep;
                $title = substr( $title, 0, -2 );
            }

            // return full title
            return get_bloginfo( 'name' ) . $custom . $title . $page_number;
        }

        /// add function 'wp_flex_title_filter()' to the
        // wp_title filter, with priority 10 and 3 args
        add_filter( 'wp_title', 'wp_flex_title_filter', 10, 3 );