If `x=a\sin2\theta(1+cos2\theta)` and `y=a\cos2\theta(1-cos2\theta)`, then prove that `1+(\frac{dy}{dx})^2=sec^2\theta`. Then show that `4acos3\theta\frac{d^2y}{dx^2}=[1+(\frac{dy}{dx})^2]^{\frac{3}{2}}`