my English teacher once told us that one of the two ways of pronouncing either is more common in BrE.
I don't remember which one is that one, /ˈē-ther/ or /ˈī-ther/?
I hope you will be able to help me,
Those phonetic transcriptions are wrong, but you seem to have made yourself understood. (It's [aI ðə])
I got the translation from the merriam-webster online dictionary, which seems not to be using IPA phonetics...
Well, to be honest, I never regard any dictionary as worth its salt if it uses anything like that popular approximation of intuitive spellings.