25. $[\mathbf{1 3}]$ Evaluate the sum
$$
\cos \left(\frac{2 \pi}{18}\right)+\cos \left(\frac{4 \pi}{18}\right)+\cdots+\cos \left(\frac{34 \pi}{18}\right) .
$$
Answer: -1 If $k18$, then the pair $\cos \left(\frac{k \pi}{18}\right)$ and $\cos \left(\frac{(36-k) \pi}{18}\right)$ also sums to 0 . So, the only term in this series that is left over is $\cos \left(\frac{18 \pi}{18}\right)=-1$.