Answer
$\theta=\{67.5^o,157.5^o,247.5^o,337.5^o\}$
Work Step by Step
$tan(2\theta)=-1$
$2\theta=tan^{-1}(-1)$
We know $tan(\theta)$ is negative in quardent $II$ and quardent $IV$
The period of the tangent function is $360^o$
$2\theta=180^o-45^o\;\;\;\;or\;\;\;\;\;\;2\theta=360^o+135^o\;\;\;\;or\;\;\;\;\;\;2\theta=360^o-45^o\;\;\;\;or\;\;\;\;\;\;2\theta=360^o+315^o$
$\theta=67.5^o\;\;\;\;or\;\;\;\;\;\;\theta=247.5^o\;\;\;\;or\;\;\;\;\;\;\theta=157.5^o\;\;\;\;or\;\;\;\;\;\;\theta=337.5^o\;\;\;$
$\theta=\{67.5^o,157.5^o,247.5^o,337.5^o\}$
