A geometry problem by Akeel Howell

Geometry Level pending

Let \(\cos{\theta} = \dfrac{\sqrt{5}-1}{2}\) for \(0 < \theta < \dfrac{\pi}{2}\) evaluate \(\sin{\theta}+\cos{\theta}\).

If this sum can be expressed in the form \(\dfrac{\sqrt{a}+\sqrt{b(\sqrt{a}-1)}-1}{2}\), find \(a+b\).

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