The value of $$\frac{\sec^2 \theta}{\cosec^2 \theta} + \frac{\cosec^2 \theta}{\sec^2 \theta} - (\sec^2 \theta + \cosec^2 \theta)$$ is:

$$\frac{\sec^2 \theta}{\cosec^2 \theta} + \frac{\cosec^2 \theta}{\sec^2 \theta} - (\sec^2 \theta + \cosec^2 \theta)$$
Put the $$\theta = 60\degree$$
= $$\frac{\sec^2 60\degree}{\cosec^2 60\degree} + \frac{\cosec^2 60\degree}{\sec^2 60\degree} - (\sec^2 60\degree + \cosec^2 60\degree)$$
= $$\frac{4}{\frac{4}{3}} + \frac{\frac{4}{3}}{4} - (4 + \frac{4}{3})$$
= 3 + $$\frac{4}{12} - \frac{16}{3}$$
= $$\frac{-24}{12}$$ = -2