An Angle Between a Line and a Plane After Projection

As shown in the figure, the equilateral triangle $A'BC$ has side length $1$. Its vertex $A'$ lies in a plane $\alpha$, while the vertices $B$ and $C$ lie on the same side of $\alpha$. Let $B'$ and $C'$ be the orthogonal projections of $B$ and $C$ onto $\alpha$, and suppose $BB' \leqslant CC'$. Let $\varphi$ denote the angle between line $CB'$ and plane $A'CC'$.

If triangle $A'B'C'$ is a right triangle with its right angle at $A'$, find the range of $\tan \varphi$.