Decent Trigonometry!

Geometry Level 2

If tanθ=34\tan \theta =\dfrac 34 for 0θπ20 \le \theta \le \dfrac \pi 2 , then cosθ2=xy\cos \dfrac \theta 2 = \dfrac x {\sqrt{y}} , where xx and yy are positive integers with yy being square-free, find x+yx + y.

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