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If tanθ=34\tan \theta =\dfrac 34tanθ=43 for 0≤θ≤π20 \le \theta \le \dfrac \pi 2 0≤θ≤2π, then cosθ2=xy\cos \dfrac \theta 2 = \dfrac x {\sqrt{y}} cos2θ=yx, where xxx and yyy are positive integers with yyy being square-free, find x+yx + yx+y.
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