If a curve is represented parametrically by the equations. \(x=\sin\left(t+\dfrac{7\pi}{12}\rig...

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If a curve is represented parametrically by the equations. \(x=\sin\left(t+\dfrac{7\pi}{12}\right)+\)\(\sin\left(t-\dfrac{\pi}{12}\right)+\sin\left(t+\dfrac{3\pi}{12}\right),\)  \(y = \cos\left(t+\dfrac{7\pi}{12}\right)+\cos\left(t-\dfrac{\pi}{12}\right)+\cos\left(t+\dfrac{3\pi}{12}\right)\) then find the value of \(\dfrac{d}{dt}\left(\dfrac{x}{y}-\dfrac{y}{x}\right)\) at \(t = \dfrac{\pi}{8}\)
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