Solve the equation on the interval $[0, 2\pi)$.
$1+\sin(\theta) = 2\cos^2(\theta)$
A) $\frac{\pi}{3}$, $\frac{4\pi}{3}$, $\frac{3\pi}{2}$
B) $\frac{5\pi}{6}$, $\frac{5\pi}{3}$, $\frac{\pi}{2}$
C) $0$, $\pi$, $\frac{\pi}{2}$
D) $\frac{\pi}{6}$, $\frac{5\pi}{6}$, $\frac{3\pi}{2}$