Mean of the square of a random unit complex number

Pick $Z$ uniformly at random on the unit circle $\{z\in\mathbb{C}:|z|=1\}$. What is $\mathbb{E}[Z^2]$?

$0$. Write $Z=e^{i\Theta}$ with $\Theta$ uniform on $[0,2\pi)$. Then $Z^2=e^{2i\Theta}$ is again uniform on the circle, and the mean of a uniform point on the circle is the centre, $0$. Equivalently, $\mathbb{E}[\cos2\Theta]=\mathbb{E}[\sin2\Theta]=0$.