If k= tan ((π)/4+1/2 cos^-1(2/3))+ tan (1/2 sin^-1(2/3)), then the number of solutions of the equation sin^-1(k x-1)= sin^-1 x- cos^-1 x is ____

If $\displaystyle k=\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{2}{3}\right)\right)+\tan \left(\frac{1}{2} \sin ^{-1}\left(\frac{2}{3}\right)\right)$, then the number of solutions of the equation $\displaystyle \sin ^{-1}(k x-1)=\sin ^{-1} x-\cos ^{-1} x$ is $\displaystyle \_\_\_\_$