I read that $ 30/\pi^2 $ can be represented as a continued fraction of the form
$$ 3 + \cfrac{1}{25 + \cfrac{16}{69 + \cfrac{81}{\ddots}}} $$
over here: http://www.ramanujanmachine.com/wp-content/uploads/2020/06/pi_square.pdf
where can I find the proof? I haven't come across such fractions before. When I looked it up, I could only find proofs for $\pi$ or $1/\pi$ but not anything to do with $1/\pi^2$.