How to solve $2\cos( \frac {\pi}3 (\theta-1)) +5=4$

Question

Im having trouble with the following problem:

solve for all theta between (0 and 2pi) and find exact values where possible for:

$$2\cos( \frac{\pi} 3(\theta-1)) +5=4$$

This is what i did:

$2\cos(\pi/3)= 1$, so

$\theta-1 = 4-5$

$\theta-1=-1$

so $\theta =0$

The answers are 3,5.

Answer 1

$$2\cos(\frac{\pi}{3}(\theta-1))+5=4\to \cos(\frac{\pi}{3}(\theta-1))=-\frac{1}{2}\to \frac{\pi}{3}(\theta-1)=2k\pi\pm\frac{2\pi}{3}\\ \to \theta=6k\pm2+1$$