The value of $$\frac{\sin \theta + \cos \theta - 1}{\sin \theta - \cos \theta + 1} \times \frac{\tan^2 \theta(\cosec^2 \theta -1)}{\sec \theta - \tan \theta}$$ is:

$$\frac{\sin \theta + \cos \theta - 1}{\sin \theta - \cos \theta + 1} \times \frac{\tan^2 \theta(\cosec^2 \theta -1)}{\sec \theta - \tan \theta}$$
Put the $$\theta = 30\degree$$,
= $$\frac{\sin 30\degree + \cos 30\degree - 1}{\sin 30\degree - \cos 30\degree + 1} \times \frac{\tan^2 30\degree(\cosec^2 30\degree -1)}{\sec 30\degree - \tan 30\degree}$$
= $$\frac{\frac{1}{2} + \frac{\sqrt{3}}{2} - 1}{\frac{1}{2} - \frac{\sqrt{3}}{2} + 1} \times \frac{\frac{1}{3}(4 -1)}{\frac{2}{\sqrt{3}} - \frac{1}{\sqrt{3}}}$$
= $$\frac{\frac{\sqrt{3}}{2} - \frac{1}{2}}{\frac{3}{2} - \frac{\sqrt{3}}{2}} \times \frac{1}{\frac{1}{\sqrt{3}}}$$
= $$\frac{\sqrt{3} - 1}{3 - \sqrt{3}} \times  \sqrt{3}$$
= $$\frac{3 - \sqrt{3}}{3 - \sqrt{3}}$$ = 1