3D bend equation derivation.

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This is how the bend work: (The number is the angle)

bend

I was searching for an equation to bend an object in a specific axis and I found one,It worked pretty well,but unfortunately I don't know why it works.

The equation is :

$$ x'= (x-\frac { 1 }{ z\theta } )\times\cos ({ z\theta })+\frac { 1 }{ z\theta } \\ y'= y\\ z'= -(x-\frac { 1 }{ z\theta } )\times\sin ({ z\theta }) $$

I want to know how they got this equation,or at least a simple explanation. and if it is already a known equation,what is its name?