Sum of Fourier Series, Sine function to Euler

Question

This might potentially be one of the dumbest question, but I'm gonna ask anyway.

view image pls

How do I get $\pi/2$? I know for a fact $e^{jθ} = cos\theta + j sin \theta$ but in this case $e^{j3\omega_0t}$... how do I find $\theta$? Btw period is given as $T_0 = 2\pi/\omega_0$

I do not know what to put on the title because I am new to this topic, so feel free to offer your suggestions

Answer 1

Notice, when $\text{z}\in\mathbb{C}$ and $\Re\left[\text{z}\right]=0$ and $\Im\left[\text{z}\right]>0$:

$$\arg\left(\text{z}\right)=\frac{\pi}{2}+2\pi\text{k}$$

Where $\text{k}\in\mathbb{Z}$ and I worked with radians.