Using the graphical method we plot y=cos2x (I'm using x instead of theta which isn't on my iPad keyboard) and y=(1/2)sinx on the same graph between x=0 and 90 degrees. For x=0, cos2x=1 (maximum) and for x=90, cos2x=-1 (minimum). For x=45, cos2x=0 (crosses the x axis). For these values of x, (1/2)sinx is 0, 1/2 (maximum) and 0.35 approx. For x=30, cos2x=1/2 and (1/2)sinx=1/4. cos2x will have twice the amplitude (height) of (1/2)sinx, but its wave is half as wide. You should find that the curves cross between 30 and 45 degrees. This can be narrowed to between 36 and 37 degrees (between 36.3 and 36.4 degrees).
Another way to solve the equation is to expand cos2x into 1-2sin^2x, so we have 1-2sin^2x=(1/2)sinx, and the quadratic: 2sin^2x+(1/2)sinx-1=0 or 4sin^2x+sinx-2=0, from which sinx=(-1+/-sqrt(1+32))8, so sinx=0.59307 approx. Therefore x=sin^-1(0.59307)=36.375 approx.