4. (25 pts) Consider a strain gage rosette mounted on the unloaded free surface of an engineering component, as shown in the figure. Note that the longitudinal strains, $\epsilon_x$, $\epsilon_y$, and $\epsilon_{45}$ are measured in the x, y, and in a third direction 45° from the other two. Develop an equation for calculating the shear strain, $\gamma_{xy}$, from the three measured strains.