Answer
Counterexample: $\displaystyle \theta=\frac{\pi}{4}$
(sample answer)
Work Step by Step
$\theta= \displaystyle \frac{\pi}{4}$ has equal sine and cosine, $\displaystyle \frac{\sqrt{2}}{2}.$
So,
LHS= $\displaystyle \sin\frac{\pi}{4}+\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}=\sqrt{2}$
LHS$\neq$RHS so the identity is not valid.