The side of the big square is $2r$ and the one of the small square is $r\sqrt{2}$, where $r$ is the radius of the circle. Then $(2r)^2=(r\sqrt{2}+2r\sin x)^2+(2r\sin x)^2$ where $x$ is the smaller of the two angles Hence $\sin x=\frac{\sqrt{6}-\sqrt{2}}{4}$ and $x=15^o$