What is the value of $$\left(\frac{4}{3}\right) \cot^2 \left(\frac{p}{6}\right) + 3 \cos^2 (150^\circ)$$ $$- 4 \cosec^2 45^\circ$$ + $$8 \sin \left(\frac{p}{2}\right)$$?

A

$$\frac{25}{4}$$

B

1

C

$$-\frac{7}{2}$$

D

$$\frac{13}{2}$$