Deriving the expectation $E\left[\left | \sum_{i=1}^N X_{i} e^{j \varphi_i} \right |\right]$

Question

When $\varphi_i$ are i.i.d. RVs that are uniformly distributed between $\left(-\frac{\pi}{a}, \frac{\pi}{a}\right)$ and $X_{i}$ are also some i.i.d RV, does the following holds? If yes, how can it be proved? $$E\left[\left | \sum_{i=1}^N X_{i} e^{j \varphi_i} \right |\right] = N \cdot E\left[X_{i}\right] \cdot E\left[\cos(\varphi_i)\right] $$