Verified Answer :

\(f(x)=2\cdot3^x+1\\ y=2\cdot3^x+1\\ 2\cdot 3^x=y-1\\ 3^x=\frac{y-1}{2}\\ x=\log_3\frac{y-1}{2}\\ f^{-1}(x)=\log_3\frac{x-1}{2}\\\)

\(\alpha_{\text{rad}}=\alpha_{\text{deg}}\cdot\frac{\pi}{180}\\ \alpha_{\text{rad}}=1600\cdot\frac{\pi}{180}\\ \alpha_{\text{rad}}=\frac{80}{9}\pi\approx27.9\)