Decent Trigonometry!

Geometry Level 3

If \(\tan \theta =\dfrac 34\) for \(0 \le \theta \le \dfrac \pi 2 \), then \(\cos \dfrac \theta 2 = \dfrac x {\sqrt{y}} \), where \(x\) and \(y\) are positive integers with \(y\) being square-free, find \(x + y\).

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