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

angle $\theta$ 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 $B C=2 A C$, the coefficient of friction is given by $\mu=\mathrm{k} \tan \theta$. The value of k is $\_\_\_\_$ .