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You can find it using rotation matrix.

get rotation matrix from transform. Each column in matrix represent unit vector along new axis. First column represent unit vector of along new x-axis.

if m0, m1, m2 are elements of first column angle between old and new x-axis is

image description

You can find it using rotation matrix.

get rotation matrix from transform. Each column in matrix represent unit vector along new axis. First column represent unit vector of along new x-axis.

if m0, m1, m2 are elements of first column column, angle between old and new x-axis is

image description image description