how to get Nearby zipcode

Most likely your values $latitude and/or $longitude are not what you expect them to be. So radians($latitdue) becomes radians() or radians('').

For getting a single row, get_row() is usually the better choice instead of get_results().

$zipdetail = $wpdb->get_row( "SELECT * FROM `li_zipcode` WHERE `zip_code` = '$zipcode'", OBJECT );

If $zipcode is coming from an untrusted source (e.g. user input), make sure to use a prepared statement:

$zipdetail = $wpdb->get_row(
    $wpdb->prepare(
        'SELECT latitude, longitude FROM `li_zipcode` WHERE `zip_code` = %d',
        $zipcode
    ),
    OBJECT
);