\(n1\ Sin\theta1=n2=Sin\theta2\)
\(Sin2\theta2=\frac{n2}{n1}Sin\theta2\)
\(2Sin\theta2\ \ \ Cos\theta2=\frac{\left(1.56\right)}{\left(1.0003\right)}Sin\theta2\)
\(Cos\theta2=\frac{\left(1.56\right)}{\left(2.0006\right)}=\)
\(\theta2=Cos^{-1}\left[\frac{\left(1.56\right)}{\left(2.0006\right)}\right]=\)
\(\theta1=2\theta2=2\left[Cos^{-1}\frac{\left(1.56\right)}{\left(2.0006\right)}\right]=77.52\)