Consider the three-dimensional Euler rotation matrix \(\hat{R}(\phi, \theta, \psi)=\) \(\hat{R}_{z}(\psi) \hat{R}_{x}(\theta) \hat{R}_{z}(\phi)\)

a. Find the elements of \(\hat{R}(\phi, \theta, \psi)\).

b. Compute \(\operatorname{Tr}(\hat{R}(\phi, \theta, \psi)\).

c. Show that \(\hat{R}^{-1}(\phi, \theta, \psi)=\hat{R}^{T}(\phi, \theta, \psi)\).

d. Show that \(\hat{R}^{-1}(\phi, \theta, \psi)=\hat{R}(-\psi,-\theta,-\phi)\).