2020 AMC 12B Question 25

For each real number $a$ with $0 \le a \le 1,$ let numbers $x$ and $y$ be chosen independently at random from the intervals $[0, a]$ and $[0, 1],$ respectively, and let $P(a)$ be the probability that $$
\sin^2(\pi x) + \sin^2(\pi y) \gt 1.
$$ What is the maximum value of $P(a)?$