On Zeros of Sums of Cosines

It is shown that there exist arbitrarily large natural numbers $N$ and distinct nonnegative integers $n_1,\dots,n_N$ for which the number of zeros on $[-\pi,\pi)$ of the trigonometric polynomial $\sum_{j=1}^N \cos(n_j t)$  is  $O(N^{2/3}\log^{2/3} N)$.