How do you find the rotation of a 3d rotation matrix Ex 0 0

How do you find the rotation of a 3d rotation matrix?

Ex:
0 0 ?1
?1 0 0
0 1 0

I found the rotation axis to be i - j - k but I do not know how to find the angle

Method to find the rotation of the matrix (taken from textbook)

(1) Translate space so that the rotation axis passes through the origin.

(2) Rotate space about the z axis so that the rotation axis lies in the xz plane.

(3) Rotate space about the y axis so that the rotation axis lies along the z axis.

(4) Perform the desired rotation by ? about the z axis.

(5) Apply the inverse of step (3).

(6) Apply the inverse of step (2).

(7) Apply the inverse of step (1).