In order to start complex differentiation we need to understand some properties of complex numbers. However I am stuck here and would appreciate some help if possible. thanks very much

If $\displaystyle 0 < \theta < \frac{\pi}{4}$, find the modulus and principal value of the argument of $\displaystyle e^{i\theta} + e^{5i \theta}$.

$\displaystyle |e^{i\theta} + e^{5i \theta}|^2 = (\cos \theta + \cos 5 \theta)^2 + (\sin \theta + \sin 5 \theta)^2 = 2 + 2 \cos 4 \theta $ so the modulus is $\displaystyle \sqrt{ 2 + 2\cos 4 \theta} $ but I don't really see how to calculate the argument and how to involve the restrictions on theta. Thanks for any help