How to get the rotation angle along Z axis in order to parallelized a plane which was rotated a certain degree along X axis to an arbitrary vector

Question

There are reference coordinates$(X,Y,Z)$, and another body coordinates$(X,y,z)$ created by rotating $30^{\circ} $ along the reference $X$ axis.

For an arbitrary vector$(x_1, y_1, z_1)$ passing $0,0,0$ of the reference coordinates, I can rotate $Z-axis$ of the reference coordinates.

Then, how can I get the rotation angle to parallelize the $X-z$ plane of the rotated body coordinates to the arbitrary vector?