What is the ruling on praying Tarawih in units of three rak'ahs, then three rak'ahs, then two rak'ahs, followed by Witr in three rak'ahs?

The prescribed manner for night prayers – whether Tarawih or other – is to pray two rak'ahs at a time, based on the Prophet's (peace be upon him) saying: "Night prayer is two by two." The method mentioned in the question has not been advocated by any scholar.