Building on works of Berthé–Steiner–Thuswaldner and Fogg–Nous, we show that the two-dimensional torus, Lebesgue almost every translation admits a natural coding such associated subshift satisfies Boshernitzan criterion. As consequence, for these torus translations, quasi-periodic potential can be approximated uniformly by one which Schrödinger operator has Cantor spectrum zero measure. We also ...