Answer
$\theta=\{201.5^o,338.5^o\}$
Work Step by Step
$2cos^2(\theta)+2sin(\theta)-1=0$
$2[1-sin^2(\theta)]+2sin(\theta)-1=0$
$2-2sin^2(\theta)+2sin(\theta)-1=0$
$2sin^2(\theta)-2sin(\theta)-1=0$
$sin(\theta)=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(2) \pm \sqrt{(2)^2 - 4 (2)(-1)}}{2(2)}=\frac{1+\sqrt{3}}{2},\frac{1-\sqrt{3}}{2}$
$sin(\theta)=\frac{1-\sqrt{3}}{2}=-0.366$
$\theta=sin^{-1}(\frac{1-\sqrt{3}}{2})$
We know $sin(\theta)$ is negative in quadrant $III$ and $IV$
$\theta=180^o-21.5^o\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=360^o-21.5^o$
$\theta=201.5^o\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;\theta=338.5^o$
$cos(\theta)=\frac{1+\sqrt{3}}{2}=1.366\;\;\;\;$
$\theta=\{201.5^o,338.5^o\}$
