A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC is smooth and…

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