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