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