404 when same slug for a custom post type and its custom taxonomy

Hello

I would like to use the same slug for a custom post type and its dedicated custom taxonomy. Bug i have 404 page on single post display and pagination (starting to second page) for taxonomy post loop.
…/books/ works fine
…/books/%post-title%/ doesn’t work
…/books/%sectors%/ works
…/books/%sectors%/page/x/ doesn’t work

Here is my code. Thanks if you can help me and tell me if this type of rewrite is possible.

add_action( 'init', 'create_sectors_taxonomies', 0 );
function create_sectors_taxonomies() {
  $labels = array(
    'name' => 'Secteurs',
    'singular_name' => 'Secteur',
    'search_items' =>  'Recherche secteur',
    'all_items' => 'Tous les secteurs',
    'parent_item' => 'Secteur parent',
    'parent_item_colon' => 'Secteur parent:',
    'edit_item' => 'Editer secteur',
    'update_item' => 'Mettre à jour le secteur',
    'add_new_item' => 'Ajouter un secteur',
    'new_item_name' => 'Ajouter un nouveau secteur',
    'menu_name' => 'Secteurs',
  );
  register_taxonomy('sectors','books', array(
    'hierarchical' => true,
    'labels' => $labels,
    'show_ui' => true,
    'query_var' => true,
    'rewrite' => array( 'slug' => 'books' ),
  ));
}
add_action('init', 'register_books');
function register_books()
{
  $labels = array(
    'name' => 'BOOKS',
    'singular_name' => 'Book',
    'add_new' => 'Ajouter un book',
    'add_new_item' => 'Ajouter un nouveau book',
    'edit_item' => 'Editer un book',
    'new_item' => 'Nouveau book',
    'all_items' => 'Tous les books',
    'view_item' => 'Voir le book',
    'search_items' => 'Rechercher un book',
    'not_found' =>  'Aucun book',
    'not_found_in_trash' => 'Aucun book dans la corbeille',
    'parent_item_colon' => '',
    'menu_name' => 'Books'

  );
  $args = array(
    'labels' => $labels,
    'public' => true,
    'publicly_queryable' => true,
    'show_ui' => true,
    'show_in_menu' => true,
    'query_var' => true,
    'rewrite' => array( 'slug' => 'books' ),
    'capability_type' => 'post',
    'has_archive' => true,
    'hierarchical' => false,
    'menu_position' => 5,
    'supports' => array('title','editor','author','thumbnail','excerpt','comments')
  );
  register_post_type('books',$args);
}