Answer: The simplest way to find the rotation angle is to take the trace of the matrix, the sum of the diagonal elements.
Step-by-step explanation: step 1 Show that the determinant is 1. Matrices with determinant -1 are reflections no rotations.
step 2 Find the eigenvalues. The three eigenvalues of the matrix are 1,e−iθ, where θ is the angle of rotation.
step 3 find the eigenvector for the eigenvalue 1. This is the axis of rotation.