trigonometry - How to compute $cos(pi / 3)$ with Angle sum and difference identities?

How to compute $\cos(\pi / 3)$ with Angle sum and difference

identities?

Hello. I am only allowed to use the Pythagorean trigonometric identity, Angle sum and difference identities, and the fact that sine and cosine are periodic functions with period $2\pi$.

I tried it like this: $$\cos(\pi/3)=\cos(\pi/6+\pi/6)=\cos(\pi/6)\cos(\pi/6)-\sin(\pi/6)\sin(\pi/6)=\cos^2(\pi/6)-\sin^2(\pi/6)$$ Can I now somehow make use of the Pythagorean trigonometric identity?