Consider a rotation around the Z axis, determined by angle $\theta$. If I change the polarity of the X or Y axis, the rotation becomes $- \theta$, and stays $\theta$ if both are inverted.
But what about if I change the polarity of the Z axis itself? Can someone help my fuzzy brain get some clarity on the matter?
Thanks
If I understand what you're asking correctly, you have a fixed point or line in $3$-$D$ space which you are rotating around the $Z$-axis. If so, then when you switch the polarity of the $Z$-axis, there's no change as such with the angle $\theta$. Instead, the difference is that there is a switch from rotating around the positive $z$ axis to now being around the negative $z$ axis, and vice versa.
However, if the point or line is represented by an equation involving the $X$, $Y$ and $Z$ co-ordinates, then there could be an effect if the $Z$ value changes to $-Z$ such that angle with the $Z$-axis is then different. In that case, then $\theta$ could change, possibly becoming $-\theta$ or even something completely different.