$$sin\theta+cos\theta=\frac{1}{\sqrt{2}}$$
$\theta =2\pi n_{1}+\frac{7\pi }{12}\text{, }n_{1}\in \mathrm{Z}$
$\theta =2\pi n_{1}+\frac{23\pi }{12}\text{, }n_{1}\in \mathrm{Z}$
