Establish the identity. \[ (\csc \theta+\cot \theta)(\csc \theta-\cot \theta)=1 \] Multiply and write the left side expression as the difference of two squares.

To establish the identity, we start by noting that the left-hand side can be expressed as the difference of two squares: \[ (\csc \theta + \cot \theta)(\csc \theta - \cot \theta) = \csc^2 \theta - \cot^2 \theta. \] Using the Pythagorean identity, we know that: \[ \csc^2 \theta = 1 + \cot^2 \theta. \] Now, substituting this into our expression gives: \[ \csc^2 \theta - \cot^2 \theta = (1 + \cot^2 \theta) - \cot^2 \theta = 1. \] Thus, we have shown that: \[ (\csc \theta + \cot \theta)(\csc \theta - \cot \theta) = 1. \] This confirms the identity is true!