Answer
$\theta=90^o\text{ or } \theta = 270^o$
Work Step by Step
Subtract $\sin^2{\theta}$ to both sides:
$0=\cos^2{\theta} +1 - \sin^2{\theta}
\\0=\cos^2{\theta}-\sin^2{\theta}+1$
RECALL:
$\cos{(2\theta)}= \cos^2{\theta}-\sin^2{\theta}$
Use the identity above to obtain:
$0=(\cos^2{\theta}-\sin^2{\theta})+1
\\0=\cos{(2\theta)}+1
\\-1=\cos{(2\theta)}$
Note that $\cos{180^o}=-1$ and $\cos{540^o}=-1$
Thus,
$2\theta=180^o \text{ or } 2\theta=540^o
\\\theta=\frac{180^o}{2} \text{ or } \theta = \frac{540^o}{2}
\\\theta=90^o\text{ or } \theta = 270^o$
