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If x = a cos3θ and y = a sin3θ, then find the value of \(\frac{d^2y}{dx^2}\) at θ = \(\frac{\pi}{6}.\)

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Given,

x = a cos3θ

Differentiating both sides with respect to θ, we get

\(\frac{dx}{d\theta}=\) - 3a cos2θ.sin θ  ...(i)

Also,

y = a sin3θ

Differentiating both sides with respect to θ, we get

\(\frac{dy}{d\theta}=\)  3a sin2θ.cos θ  ...(ii)

Now,

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