A small block starts slipping down from a point B on an inclined plane A B , which is making an angle θ…

A small block starts slipping down from a point $B$ on an inclined plane $AB$, which is making an angle $\mathrm{\theta }$ with the horizontal section $BC$ is smooth and the remaining section $CA$ is rough with a coefficient of friction $\mu$. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $BC\mathit{=}\mathit{2}AC$, the coefficient of friction is given by $\mathrm{\mu }=\mathrm{k} \mathrm{tan\theta }$. The value of $k$ is .......