I don't doubt that the OP has an Italian threaded BB, but in his words he believes its Italian threaded. I posted warning of the possibility of BSC threading, because I've seen too many people incorrectly assume Italian frames are 36x24 RH threaded and work amazingly hard tightening cups they wanted to remove.
I'm of the "measure twice, cut once" school so offered a "safe" way to be sure of what people were dealing with. All left cups have RH threads, so if there's the least possible doubt, at least that's reliable.
BTW- nothing is safe. I once had the "pleasant" surprise of removing an Italian threaded BB from a British built bike. Go figure!!
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