You can use what is called a "pipe extractor" which is an
EZOut type tool that is specifically made to remove broken
nipples.

Here is a picture of one that is the wrong size for your application:

http://www.heavydutystore.com/Ridgid...r_p_21796.html

They are usually available at a "real" plumbing store. I have never seen them at a Depot

mike in tucson