For which we use the following formula \(n_1=Sin\theta=n_2\ Sin\theta_2\)
We clear from the following formula
\(n_1Sin\ \theta_1=Sin\ 2\theta_2=\frac{n_2}{n_1}\ Sin\theta_2\)
We substitute the values
\(Sin\theta_2\ Cos\theta_2=\frac{\left(1.56\right)}{\left(1.0003\right)}Sin\theta_2\)
\(Cos\theta_2=\frac{\left(1.56\right)}{\left(2.0006\right)}\)
\(\theta_2=Cos^{-1}\left[\frac{\left(1.56\right)}{\left(2.0006\right)}\right]\)
which gives us result like the following
\(\theta_1=\ 2\theta_2=\ 2\left[Cos^{-1}\frac{\left(1.56\right)}{\left(2.0006\right)}\right]\)\(=77.52ยบ\)