[UPSC IFoS 2012] Angular momentum, spin etc (Q313, 20M)

(i) Show that the orientation of the spin angular momentum vector of an electron with respect to the z-axis is less than one radian for spin up electron. (ii) When the orbital angular momentum vector \vec{L} has the magnitude \sqrt{6}\hbar, calculate the L_z components. What angles does the \vec{L} vector make with the z-axis ?