Suppose $\theta_1,\theta_2,\cdots, \theta_n$ are independent and identically distributed (i.i.d.) real-valued random variables and here we specifically consider the uniform distribution in the interval $[0,1]$. Then how to calculate the expected value of the following variable which is function of $\theta_1,\theta_2,\cdots, \theta_n$.
The target variable is: $|e^{j 2\pi(\theta_1-\theta_2)}+e^{j 2\pi(\theta_3-\theta_4)}+\cdots+e^{j 2\pi(\theta_{n-1}-\theta_n)}|$.
Here, $e$ is the base of the natural logarithm, $j^2=-1$ and $|\cdot|$ is the absolute value symbol.
About: This is not a homework problem. I met it when I try to calculate the expectation of $|g\star g|$, where $\star$ is the correlation operator and $|\cdot|$ represents element-wise absolute. $g$ ($g_{i,j}=e^{j2\pi\theta_{i,j}}$) is an $N\times N$ complex-valued random matrix, where $\theta_{i,j}$ are i.i.d. real random variables,