Calculus problem #2154

Calculus Level 3

A curve is defined by (x,y)=(cos3θ,sin3θ)(x,y) =\left(\cos^3 \theta, \sin^3 \theta \right). If the equation for the tangent line at θ=23π\theta=\frac{2}{3}\pi is y=ax+by=ax+b, what is the value of a×b a \times b ?

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