The trigonometry thing is simply a marketing gimmick for this proof. There is no more or less trigonometry in this proof than there is in Einstein's proof. In fact, they could just as well have taken Einstein's construction and reformulated that proof in their language by using sine rule instead of similar triangles. But then the gimmick would be too obvious.

Somehow the second gimmick (the infinite series construction instead of Einstein's elegant and simple construction) makes our monkey brains not notice the first gimmick.