Answer
The solutions are:
$45^o, 90^o, 225^o, 270^o$
Work Step by Step
The given equation can be solved by graphing.
Treat each side of the equation as a function, so graph $y=\sin{(2\theta)}$ and $y=\cos{(2\theta)}+1$.
The first coordinate of the points of intersection are the solutions to the given equation.
Note that:
$\frac{\pi}{4}=45^o
\\\frac{\pi}{2}=90^o
\\\frac{5\pi}{4}=225^o
\\\frac{3\pi}{2}=270^o$
(Refer to the graph below.)
