Show that any path starting from (0,0) must be the constant path.

Question

Let $Z=\{(x,\sin(\frac{\pi}{x})\mid 0<x\leq1\}$, and suppose $X=Z\bigcup\{(0,0)\}$ is equipped with the subspace topology. Show that any path in $X$ starting from $(0,0)$ must be the constant path.