How is "shimatta" used? And is it casual or very informal?
Can one actually use this without getting dirty looks?

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"shimatta" is like "oops" or  "oh dear" in English and have the nuance "how stupid of me".

For my impression, it is casually used among close frineds. But in formal situation, you had better not use it, for it may leave rude impression to others.

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"shimatta"
you can use it when you make mistakes.

for my opinion, i dont think i use this impression very often.

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shimatta is oops. May be just informal.