$11-3.$ The assembly is used for exercise. It consist of four pin$-$connected bars, each of length $\backslash ($ L $\backslash ),$ and a spring of stiffness $\backslash ($ k $\backslash )$ and unstretched length $\backslash ($ a$(<mn>2</mn>$ L$)\backslash ).$ If horizontal forces $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ and $\backslash (-\backslash$mathbf$\{$P$\}\backslash )$ are applied to the handles so that $\backslash (\backslash$theta $\backslash )$ is slowly decreased, determine the angle $\backslash (\backslash$theta $\backslash )$ at which the magnitude of $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ becomes a maximum.

Prob. $11-3$