Is there any special when all Fourier components have the same angle?
sine waves all have zero crossings at the same phase of $0$ or $\pi$ and have a peak (or valley) with a phase of $\pm\tfrac{\pi}{2}$.

cosine waves all have zero crossings at the same phase of $\pm\tfrac{\pi}{2}$ and have a peak (or valley) with a phase of $0$ or $\pi$.

so if it's a $\sin(\cdot)$ series (with no cosine terms), expect a big zero-crossing when all of the phases line up at $0$ or $\pi$.  

or expect a $\cos(\cdot)$ series (with no sine terms) to have a major zero-crossing transition to occur when the phases are $\pm\tfrac{\pi}{2}$.