If you ~ a cloth or a piece of clothing, you hold it by one of its edges and move it up and down one or more times, in order to open it out, make it flat, or remove dust.
While the water was heating she decided to ~ the carpet...
I took off my poncho, shook it out, and hung it on a peg by the door.
PHRASAL VERB: V P n (not pron), V n P
see also shake-out