$7\mathrm{.}146$ The rosette shown has been used to determine the following strains at a point on the surface of a crane hook:

${}_1=+420{10}^{-6}in\frac{.}{i}n.{}_2=-45{10}^{-6}in\frac{.}{i}n.$

${}_4=+165{10}^{-6}in\frac{.}{i}n.$

$($a$)$ What should be the reading of gage $3?($b$)$ Determine the principal strains and the maximum in$-$plane shearing strain.