Solution (source code)

= Solution

Along $x=\sin s$ and $t=s^2$, the characteristic expression is
$$
(1-\sin^2s)(2s)^2=4s^2\cos^2s.
$$
It vanishes exactly when
$$
s=0\quad\hbox{or}\quad s=\frac\pi2+k\pi\quad(k\in\mathbb Z).
$$