Salem's problem for the inverse Minkowski $?(t)$ function

Let $d_n$ be the coefficient Fourier–Stieltjes of the Minkowski $?(t)$ function –
$$ d_n=\int^1_0\cos2\pi nt\,d?(t). $$
Salem's problem is as to whether $d_n$ tends to zero as $n\to\infty$.
In the paper the coefficient Fourier
$$ \alpha_n=\int^1_0\cos(2\pi n?(t))\,dt $$
is considered. It is proved that $\alpha_n$ does not tend to zero as $n\to\infty$.