Answer
$0,\frac{\pi}{4},\frac{5\pi}{4}$
Work Step by Step
1. $(tan\theta-1)(sec\theta-1)=0 \Longrightarrow tan\theta=1\ or\ sec\theta=1\ (cos\theta=1)$,
2. $cos\theta=1 \Longrightarrow \theta=0$ in $[0,2\pi)$,
3. $tan\theta=1 \Longrightarrow \theta=\frac{\pi}{4},\frac{5\pi}{4}$ in $[0,2\pi)$.
