Summary: An important result of Weyl states that for every sequence \((n_k)_{k\geq 1}\) of distinct positive integers the sequence of fractional parts of \((n_k \alpha)_{k\geq 1}\) is u.d. \(\mod 1\) for almost all \(\alpha\). However, in this general case it is usually extremely difficult to measure the speed of convergence of the empirical distribution of \((\{n_1 \alpha \}, \cdots, \{n_N \alpha \})\) towards the uniform distribution. In this paper we investigate the case when \((n_k)_{k \geq 1}\) is the sequence of evil numbers, that is the sequence of non-negative integers having an even sum of digits in base 2. We utilize a connection with lacunary trigonometric products \(\prod_{\ell=0}^L \left|\sin \pi 2^\ell\alpha \right|\), and by giving sharp metric estimates for such products we derive sharp metric estimates for exponential sums of \(\left(n_k \alpha\right)_{k \geq 1}\) and for the discrepancy of \(\left(\left\{n_k \alpha \right\} \right)_{k\geq 1}\). Furthermore, we provide some explicit examples of numbers \(\alpha\) for which we can give estimates for the discrepancy of \(\left(\left\{n_k \alpha\right\}\right)_{k\geq 1}\).