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Showing Taxonomy Terms in RSS Feed

The problem:
I have a custom post type “announcements” and a custom taxonomy “announcements_taxonomy”. I can access the rss feed by going to http://domain.com/announcements/feed – The problem is I am can not see the categories/tags in the RSS feed.

Detail:
I am using Simplepie to get the feed items and show them outside of a WordPress install. Because the rss feed on my WP site does not show the categories I can not access them with Simple pies get_categories() function.

Question:
How can I get categories from my custom post type and taxonomy to show in the rss feed?