Asymptotic average of cosine function

Question

I am wondering whether the following equality is true and how it can be proved:

$$ \lim_{T \to \infty} \frac{1}{T} \sum_{t=1}^T \cos(2t)=0. $$

Answer 1

Hint: $\cos(2t) = \Re (e^{i 2t})$. The series can therefore be considered a geometric series.