Let $$ \frac{\pi}{2} < \theta < \pi $$ and $$\cot\theta=-\frac{1}{2\sqrt{2}}.$$ Then the value of $$\sin\left( \frac{150}{2}\right)\left(\cos 80 + \sin 80\right)+\cos\left( \frac{150}{2}\right)\left(\cos 80 - \sin 80\right)$$ is equal to

A

$$-\frac{\sqrt{2}}{\sqrt{3}}$$

B

$$\frac{\sqrt{2}}{\sqrt{3}}$$

C

$$\frac{\sqrt{2}-1}{\sqrt{3}}$$

D

$$\frac{1-\sqrt{2}}{\sqrt{3}}$$