Is there any "home remedy" to getting a broken off trem arm piece out of the hole, or is it a trip to the guitar repair shop? Thanks.

is it a snap-in or screw-in arm?

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Don't worry, Be happy.

I had a screw in vibrato arm crack off inside the block and endedup having to get a new block as the diameter of the screw was too small to use an Easy-Out.I had unwisely put the guitar in the case with the arm screwed in and someone dropped the case facedown and the arm snapped right where it goes into the block.There's a little warning Never Never put the guitar in the case with the arm screwed in.

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'65 Strat,65 Mustang,65 Jaguar,4 more Strats,3 vintage Vox guitars,5 Vox amps,'69 Bassman with a '68 2-15 Bassman cab,36 guitars total-15asst'd amps total,2 vintage '60s Hammond organs & a myriad of effects-with a few rare vintage ones.

If it is a screw in usually a very small drill bit, but I would still have a pro tech do it.