How to perform extrinsic rotations

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I have a point $(1,2,0)$ and I want to rotate it around the global $x$ axis by $45^{\circ}$, and around the global $y$ axis by $60^{\circ}$ and $0^{\circ}$ around the global $z$ axis.

How exactly can I do this?

Please show all of the exact matrices used in the multiplication and how they are formed. I am only a new a level student and have only really learnt about the basic $3d$ rotation matrices, and I need this for a Rubik's cube game.

An example of this can be found on the following website/article:

What I need: second plane animation

What I don't want: first plane animation