Consider the general orientation of three strain gages at a point as shown. Write a computer program that can be used to determine the principal in-plane strains and the maximum in-plane shear strain at the point. Show an application of the program using the values \(\theta_{a}=40^{\circ}, \epsilon_{a}=160\left(10^{-6}\right), \theta_{b}=125^{\circ}\), \(\epsilon_{b}=100\left(10^{-6}\right), \theta_{c}=220^{\circ}, \epsilon_{c}=80\left(10^{-6}\right)\).