How to solve $\cos(\theta + angle)$ equation?

Question

I can't seem to figure out how to solve an equation similar to the one below.

$$cos(\theta+\frac{\pi}{3})=\frac{1}{\sqrt{3}}$$

The steps I have taken so far are shown below. From there I would just solve for $\theta$, however after checking my answer with Woflram Alpha, I appear to have done something wrong.

$$\theta+\frac{\pi}{3}=\arccos(\frac{1}{\sqrt{3}})$$

Am I missing a step when solving this equation?

Answer 1

Your step is ok, but it misses the "second" solution: $$\theta+\frac{\pi}{3}=\pm{arccos(\frac{1}{\sqrt{3}}})$$ Move the $\pi/3$ over and you are done! (You may add the multiplicity of $2\pi$ if needed)

Answer 2

$$\cos(a+b) = \cos a\cos b - \sin a\sin b$$$$=\cos\theta\cos\frac\pi 3 - \sin\theta\sin\frac\pi 3$$

Try going off of this.