Question 4.6: One reason why the $R_\hat{n}(θ)$ operators are referred to as rotation operators is the following fact, which you are to prove. Suppose a single qubit has a state represented by the Bloch vector $λ$. Then the effect of the rotation$ R_\hat{n}(θ)$ on the state is to rotate it by an angle $θ$ about the $\hat{n}$ axis of the Bloch sphere. This fact explains the rather mysterious looking factor of two in the definition of the rotation matrices.
In this question $\hat{n} = (n_x, n_y, n_z)$ is a unit vector in three dimension and we have $R_\hat{n}(θ) = cos(\theta/2) I - isin(\theta/2)(n_xX + n_yY + n_zZ)$
I don't understand the idea of this question? I need some explanation of this question.