How do I change the 3DS eShop region?

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I got a 3DS XL for Christmas. However, the only things on the eShop in Costa Rica are updates! I can't change my NNID region, and the eShop refuses to load when the NNID region and 3DS profile region don't match. How do I change the region without deleting my NNID?
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Quick Answer about "How do I change the 3DS eShop region?"
Is the 3DS eShop region locked?
Yes, the Nintendo 3DS, Nintendo 3DS XL, Nintendo 2DS, New Nintendo 3DS, New Nintendo 3DS XL, and New Nintendo 2DS XL systems are region locked. Region locking enables Nintendo to include parental controls and more efficiently deliver region-specific system and menu updates to users.How do you bypass the Nintendo eShop region?
What can I do if Nintendo eShop is unavailable to my region?What happens if you change region on 3DS?
If you change your country settings, you will no longer be able to use services that require a Nintendo Network ID, such as browsing Nintendo eShop or posting to Miiverse.Can you play online with a region Change 3DS?
3DS cares more about the region of the game, not region of the console. IE if you have a US copy of the game and you region change to EU (assuming you are using custom firmware to perform the region change), then you will still only connect to US servers.\
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: David McBee, David McBee, Brett Sayles, Pixabay