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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