Tessellate S.T.E.M.S (2019) - Physics - Category C - Set 1 - Objective Problem 3

At given instant of time, a rigid rotator is in the state $\psi(\theta, \phi) = \sqrt{3/4\pi}\sin\theta \sin\phi$ , where $\theta$ is the polar angle relative to the z-axis and $\phi$ is the azimuthal angle. Measurement will find which of the following possible values for the z-component of the angular momentum $L_z$ ?