Systems of Differential Equations · Superchallenge problem

Let $\mathbf x'=A\mathbf x$ with $A=\begin{pmatrix}0&-1&1\\1&0&-1\\-1&1&0\end{pmatrix}$ and $\mathbf x(0)=(1,0,0)$. Find the first time $t>0$ at which $\mathbf x(t)=(0,1,0)$.