Using $$\cosec \left(\alpha + \beta \right) = \frac{\sec \alpha \times \sec \beta \times \cosec \alpha \times \cosec \beta}{\sec \alpha \times \cosec \beta + \cosec \alpha \times \sec \beta}$$, find the value of $$\cosec 75^{\circ}$$.

A

$$\frac{\sqrt{6} + \sqrt{2}}{4}$$

B

$$\frac{\sqrt{6} - \sqrt{2}}{4}$$

C

$$\sqrt{6} - \sqrt{2}$$

D

$$\sqrt{6} + \sqrt{2}$$