If $$\sin \theta+\cos \theta=\sqrt{5}\sin(90-\theta)$$, find the value of $$\cot \theta$$.

A

$$\frac{\sqrt{5}-1}{5}$$

B

$$\frac{\sqrt{5}+1}{4}$$

C

$$\frac{\sqrt{5}+1}{3}$$

D

$$\frac{\sqrt{5}-1}{4}$$