Let \(X(t)=A(t) \sin (\omega t+\Phi)\) where \(A(t)\) and \(\Phi\) are independent, non-negative random variables for all \(t\), and let \(\Phi\) be uniformly distributed over \([0,2 \pi]\).

Verify: If \(\{A(t), t \in(-\infty,+\infty)\}\) is a weakly stationary process, then the stochastic process \(\{X(t), t \in(-\infty,+\infty)\}\) is also weakly stationary.