If $$2 \sin (3x - 15)^\circ = 1, 0^\circ < (3x - 15) < 90^\circ$$, then find the value of $$\cos^2 (2x + 15)^\circ + \cot^2 (x + 15)^\circ$$.

A

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

B

$$1$$

C

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

D

$$\frac{5}{2}$$