Tangled with differentials

Calculus Level 4

If x=tcostx = t \cos t and y=t+sinty = t + \sin t, then find d2xdy2\dfrac{d^2x}{dy^2} at t=π2t = \dfrac \pi 2.

If the answer is in the form (1)a(π+bc)(-1)^a \left(\dfrac{π + b}{c}\right), where aa is the smallest possible whole number satisfying the solution and bb and cc are natural numbers, input the answer as a+b+ca+b+c.

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