To find the stationary point, we need to differentiate \(y = \sin x \sin 2x\) and set the derivative to zero.

Using the product rule, \(y' = \cos x \sin 2x + 2 \sin x \cos 2x\).

Using the double angle formula \(\sin 2x = 2 \sin x \cos x\), we can express the derivative in terms of \(\sin x\) and \(\cos x\).

Equating the derivative to zero, we obtain \(3 \sin^2 x = 2\), which simplifies to \(\tan^2 x = 2\).

Solving for \(x\), we find \(x = 0.955\) (to 3 significant figures).