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Geometry Level 2

{sinθx=cosθycos4θx4+sin4θy4=97sin2θx3y+y3x \begin{cases} \dfrac{\sin\theta}{x} =\dfrac{\cos\theta}{y} \\ \dfrac{\cos^{4}\theta}{x^{4}}+\dfrac{\sin^{4}\theta}{y^{4}}=\dfrac{97\sin 2\theta}{x^{3}y+y^{3}x} \end{cases}

Let xx and yy be positive real numbers and θ\theta is an angle such that it is not a multiple of π2\frac{\pi}{2}. If x,yx,y and θ\theta satisfy the system of equations above, find xy+yx\dfrac{x}{y}+\dfrac{y}{x}.


Source: 2009 Harvard-MIT Mathematics Tournament
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