Curves & Motion · Superchallenge problem

Viviani's curve $\mathbf r(t) = \left(1 + \cos t,\ \sin t,\ 2\sin\tfrac t2\right)$, $0 \le t \le 4\pi$, lies on the sphere $x^2 + y^2 + z^2 = 4$. Find the ratio of its largest curvature to its smallest curvature.