The fundamental period of the function f(θ) = tan3θ is:

The tangent repeats every 180° in its own argument, so the values return when 3θ grows by 180° — that is, when θ grows by 60°. Quoting 180° forgets the inner 3 altogether, 120° uses 360° instead of the tangent's 180°, and 540° multiplies by 3 where one should divide.