12.1.12 Olympic geometry

Problem: Square \( A B C D \) is inscribed in the circle \( \omega \). On the smaller \( \operatorname{arc} C D \) of the circle \( \omega \) an arbitrary point \( M \) is chosen. Inside the square such points as \( K \) and \( L \) are marked inside the square so, that \( K L M D \) is a square. Find \( \angle A K D \).