Probably related. < *fay-t-at-, the first -t- understood as part of the stem to which a second feminine suffix -at was attached ?. Cp. also faytata ‘to have illicit intercourse’ (WTS 666).
Tigrinya
faytätä - to give oneself to bad life, prostitution (of a woman) and libertinage (of a man)
(Bass. 1011)