Angle optimisation problem in 3 dimensions.

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I came across this question in test.

Given $A(0,0,1), B(2,1,2)$ be two points in 3-D space also P($\alpha ,\beta$) ($\alpha>0 ,\beta>0$) be a point on the xy-plane such that $\angle APB$ is maximum, then find $\alpha,\beta$

I tried ploting those points roughly in space and then tried to express the angle in terms of $\alpha,\beta$ but since its 3-D I am finding it hard to imagine there position.also the equations i got are too complicated (probably wrong) so i am not mentioning them here.

I wanted to know if there is a simplier method.

Welcome in advance!!

REGARDS!