Layla was accustomed to lying to such an extent that she spoke the truth only on one day in a week. She, once, made one statement a day on three consecutive days.
Day 1: "I don't speak the truth on Mondays and Tuesdays."
Day 2: "It's either Thursday, Saturday or Sunday today."
Day 3: "I blatantly tell lies on Fridays and Saturdays."
From these three statements, deduce the day of the week when Layla actually speaks the truth. Provide a detailed solution along with your answer.