$-1=\cos(t)+\cos^2(t)-\sin^2(t)=\cos(t)+2\cos^2(t)-1$
$0=\cos(t)+2\cos^2(t)$
Let $u=\cos(t)$
$0=2u^2+u =u(2u+1)$
$u=0 \vee u=-\dfrac 1 2$
$\cos(t)=0 \Rightarrow t=\dfrac {\pi}{2} + \pi k, ~k \in \mathbb{Z}$
$\cos(t)=-\dfrac 1 2 \Rightarrow t = \dfrac {2\pi}{3}+2\pi k \vee t=\dfrac{4\pi}{3} + 2\pi k, ~k\in \mathbb{Z}$