Worth saving a broken tap?

Anyone have advice for extracting a broken tap? I foolishly bought the #2-56 tap on Amazon that includes a #51 bit and the tap snapped on my second use. This is not my first time tapping, but the first time I've tapped something that wasn't a through-hole, and my first time tapping this small.
I've considered trying to send the #51 back through, not sure how that will go, but might give that a go. I've also considered snipping off about 2mm of the post to try to grab what's left of the tap and try to back it out that way. Thoughts?
Thanks in advance!
Discussion
That happened to me when I tried tapping my first time. Just had to toss it and try again.
But gotta say that whole episode turned me off of tapping for cars in general. Now I just drill a hole and just twist in the screws without the hole being tapped. It will self-tap since the metal is already pretty soft. Maybe less reliable but a lot easier!
Theoretically, the tap is harder than the drill bit. You will have little luck drilling that broken tap with a drill bit you used to make the hole. It would have to be a smaller diameter... and hardened. I don't think they make easy-outs that small... at least I have not seen it.
My 2 cents... worth a lot less these days unless they are real copper pennies!
FredD
saw the post around, grab cut piece of post/tap, attempt to remove by squeezing post stub with pliars, and unscrew
unscrews, celebrate, or
break tap again, yell loudly, throw casting across room, purchase replacement TV, new tap, and new casting
start again
dr
What I have done when this happens is cut down the post a little bit with side cutters to expose the broken piece of the tap enough to grab with vise grips and rotate the broken tap out of the post. Then use a spacer to put between the base and the now shorter post. It also necessitates the use of a longer screw to hold the car together.
grind the broken tap flat as a bottomer
the reason taps and drills break?
not sharp/cheap
too much too fast,
a 2- 56 in a 51 hole, use a pin vice for the tap, 1/4-1/2 turn in, back it out, clear chips, repeat
I don't buy nuts on many projects, I just drill the hole, and tap it, or make a retainer
NO LUBE on non ferrious metals, slow and easy, if it feels tight you already went too far
and determine your bottom, bottom out a tap good luck easing it back out but you can do it
dr
Throw it away. Purchase another. Be gentle. Drink beer.