Correct spelling for the English word "betine" is [bɪtˈiːn], [bɪtˈiːn], [b_ɪ_t_ˈiː_n] (IPA phonetic alphabet).
There isn't a clear etymology for the word "betine" as it doesn't exist in English vocabulary or have a widely recognized meaning. It's possible that "betine" is a misspelling or a rare term specific to a particular context or regional dialect. Without more information or context, it is difficult to give a precise answer to its etymology.