Answer
$\frac{3\pi}{8},\frac{7\pi}{8},\frac{11\pi}{8},\frac{15\pi}{8}$
Work Step by Step
1. $cos^2(\theta)+2sin\theta cos\theta-sin^2\theta=0\Longrightarrow cos(2\theta)+sin(2\theta)=0\Longrightarrow tan(2\theta)=-1$
2. For $tan(2\theta)=-1$, we have $2\theta=k\pi+\frac{3\pi}{4}$ thus $\theta=\frac{k\pi}{2}+\frac{3\pi}{8},$
3. Within $[0,2\pi)$, we have $\theta=\frac{3\pi}{8},\frac{7\pi}{8},\frac{11\pi}{8},\frac{15\pi}{8}$
