If $$2k \sin 30^{\circ} \cos 30^{\circ} \cot 60^{\circ} = \frac{\cot^{2}30^{\circ}\sec 60^{\circ}\tan 45^{\circ}}{\cosec^{2}45^{\circ}\cosec^{2}30^{\circ}}$$, then find the value of k.

A

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

B

3

C

1

D

6