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The most polite form of this is probably "I don't give a darn." (or "I don't give a hoot" -- but either one is "safe for children").

The rudest form in common use is "I don't give a f*ck"

And...

If I'm not mistaken, трын is a corrupted form of тын, an old word for "a fence" (for which забор is now the usual term).

So тын-трава was "grass that grows by the fence" -- in other words, useless...

Note that Мне плевать literally implies "It's for me to spit on" while Мне пофиг is very roughly "I show it the middle finger". (Because фиг is the name of a rude hand gesture).

Or, as Shakespeare...