Curves & Motion · Hard problem

A particle moves along the helix $\mathbf r(t) = \left(2\cos t,\ 2\sin t,\ \sqrt5\,t\right)$, starting at $(2, 0, 0)$ when $t = 0$. Find its $z$-coordinate after it has travelled a distance of $6\pi$ along the helix. Give an exact answer.