The curve L is given by the parametrization:
$x(t)=t\cos(2t), y(t)=t\sin(2t), z(t)=\frac{4}{3}t\sqrt{t}$ while $0 \le t \le 3\pi$.
How many times does this curve cut the plane $y=2$?
I'm not sure if there's a fixed way to solve these type of questions, but what I thought about is if L is gonna cut $y=2$, then that's whenever $t\sin(2t)=2$, but tbh I got a little stuck in how should I find $t$ values from this equation?
Any help is really appreciated, thanks in advance!