Let \( x(t)=2\sqrt{2}\cos t\,\sqrt{\sin 2t} \) and \( y(t)=2\sqrt{2}\sin t\,\sqrt{\sin 2t} \), \( t\in\left(0,\dfrac{\pi}{2}\right) \). Then \(\displaystyle \dfrac{1 + \left(\dfrac{dy}{dx}\right)^2}{\dfrac{d^2y}{dx^2}}\) at \( t=\dfrac{\pi}{4} \) is equal to:
