trigonometric expression in phased array
I believe you are asking

why is \$\theta = 90^\circ - \varphi \$?

This is actually a purely math specific question, so perhaps you should have asked it mathematics stack exchange instead. Anyway have a look of the sketches below

It should be clear that
$$90^\circ = \theta+\varphi $$
Which simply becomes
$$90^\circ-\varphi = \theta $$
Does that answer your question?