The Unit Circle and Circular Functions · Superchallenge problem

Evaluate exactly: $\displaystyle\sum_{k=1}^{2026}\cos\dfrac{k\pi}{3}=\cos\dfrac{\pi}{3}+\cos\dfrac{2\pi}{3}+\cos\dfrac{3\pi}{3}+\cdots+\cos\dfrac{2026\pi}{3}$.