Numerical Methods: Euler to Runge–Kutta · Superchallenge problem

The trapezoidal (Crank–Nicolson) method $\mathbf{u}_{n+1} = \mathbf{u}_n + \dfrac{h}{2}\left(F(\mathbf{u}_n) + F(\mathbf{u}_{n+1})\right)$ is applied to the oscillator $x' = y$, $y' = -x$ from $(1, 0)$ with step $h = 2\sqrt{3}$. The numerical solution turns out to be exactly periodic. What is its period, i.e. the smallest time $T > 0$ at which the computed point returns to $(1, 0)$?