Second Derivative of Parametric Equation

Calculus Level 3

Let x,y:RRx,y : \mathbb{R} \to \mathbb{R} be functions satisfying y(t)=sin2ty(t) = \sin^2 t and x(t)=costx(t) = \cos t for all tt. The second derivative d2ydx2\frac{d^2 y}{d x^2} is a constant function, equal to aa everywhere. Find the value of aa.

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