Let $C$ be the circle in the complex plane with centre $z_0=\tfrac{1}{2}(1+3i)$ and radius $r=1$. Let $z_1=1+i$ and the complex number $z_2$ be outside the circle $C$ such that $\lvert z_1-z_0\rvert\,\lvert z_2-z_0\rvert=1$. If $z_0,z_1$ and $z_2$ are collinear, then the smaller value of $\lvert z_2\rvert^2$ is equal to: