If \( y = y(x) \) satisfies the differential equation \( 16\left(\sqrt{{x}+{9}+\sqrt{x}}\right)\!\left(4+\sqrt{9+\sqrt{x}}\right)\cos y\,dy = (1+2\sin y)\,dx,\ x>0 \) and \( y(256)=\frac{\pi}{2},\ y(49)=\alpha \), then \( 2\sin\alpha \) is equal to:
\( \sqrt{2}-1 \)
\( 2\sqrt{2}-1 \)
\( 2(\sqrt{2}-1) \)
\( 3(\sqrt{2}-1) \)
