Given that a series {$x_t$} where $x_t=sin(t+U)$, $U$ has uniform distrubution on $(0,2\pi)$.
Now $E(U)=\pi$, $var(U)=\frac{\pi^2}{3}$, I noticed that $sin(x)$ is a periodic function, $U$ is from $0$ to $2\pi$, so is there some useful information?
Here I think it is hard to find the p.d.f of this $sin(\cdot)$ function or using Taylor's expansion. Can anyone help me with that?
Thank you in advance!