The value of $$\frac{\sec^2 60^\circ \cos^2 45^\circ + \cosec^2 30^\circ}{\cot 30^\circ \sec^2 45^\circ - \cosec^2 30^\circ \tan 45^\circ}$$ is:

$$\frac{\sec^260^{\circ}\cos^245^{\circ}+\operatorname{cosec}^230^{\circ}}{\cot30^{\circ}\sec^245^{\circ}-\operatorname{cosec}^230^{\circ}\tan45^{\circ}}=\frac{\left(2\right)^2.\left(\frac{1}{\sqrt{2}}\right)^2+\left(2\right)^2}{\left(\sqrt{3}\right)\left(\sqrt{2}\right)^2-\left(2\right)^2.\left(1\right)}$$

$$=\frac{4\times\frac{1}{2}+4}{2\sqrt{3}-4}$$

$$=\frac{6}{2\sqrt{3}-4}$$

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

$$=\frac{3}{\sqrt{3}-2}\times\frac{\sqrt{3}+2}{\sqrt{3}+2}$$

$$=\frac{3\left(\sqrt{3}+2\right)}{3-4}$$

$$=-3\left(2+\sqrt{3}\right)$$

Hence, the correct answer is Option A