Question

$$\sin\ \theta=\frac{\sqrt{2}}{2}$$

Solve for θ (complex solution)

$\theta =2\pi n_{1}+\frac{\pi }{4}\text{, }n_{1}\in \mathrm{Z}$
$\theta =2\pi n_{1}+\frac{3\pi }{4}\text{, }n_{1}\in \mathrm{Z}$

Solve for θ

$\theta =2\pi n_{1}+\frac{\pi }{4}\text{, }n_{1}\in \mathrm{Z}$
$\theta =2\pi n_{2}+\frac{3\pi }{4}\text{, }n_{2}\in \mathrm{Z}$