Answer
The equation is not an identity.
A counterexample: $\theta=0.$
Work Step by Step
Graphing utility used: online calculator, desmos.com.
(see below)
The graphs of the two expressions are not equal,
implying that the equation is not an identity.
A counterexample is $\theta$=0, for which
LHS=$\displaystyle \frac{1-1}{1}=0$
RHS=$\displaystyle \frac{1}{1+1}=\frac{1}{2}$
LHS$\neq$RHS, so the equation is an identity