MYSQL: select all items in specific exhibit

I'm trying to select (via MySQL) all the items used in 2 specific exhibits (using their exhibit_id values) and set those items to public but can't quite figure it out.

I know the syntax is bad in the semi-psuedo-code below, but this is how I'm thinking about it. What is the better/correct way to approach this? (obviously, I don't do much with MySQL).

// set pages variable: select all pages in desired exhibits
SELECT @pages := id FROM omeka_exhibit_pages WHERE exhibit_id =111 OR exhibit_id =112;

// set items variable: select all items from exhibit pages matching the pages selected above
SELECT @items := item_id FROM omeka_exhibit_page_entries WHERE item_id =@pages;

// set the selected items to public
UPDATE omeka_items SET public=1 WHERE id=@items

I ended up doing this in separate steps, each of which yielded a series of numeric IDs:

Get page IDs...

SELECT id FROM omeka_exhibit_pages WHERE exhibit_id=[id of the exhibit]

Use page IDs to get item IDs...

SELECT item_id FROM omeka_exhibit_page_entries WHERE page_id in ([comma separated list of results from previous step]) AND item_id is not null

Use item IDs to update items...

UPDATE omeka_items SET public=1 WHERE id in ([comma separated list of results from previous step] )

Since I only had to do this twice it wasn't a big deal. Nonetheless, if anyone wants to share a better approach, that would be awesome.