Let the function f : 0 , π → ℝ be defined by f θ = sin θ + cos θ 2 + sin…

Let the function $f:\left(0,\pi \right)\to \mathrm{ℝ}$ be defined by $f\left(\theta \right)={\left(\sin \theta +\cos \theta \right)}^2+{\left(\sin \theta -\cos \theta \right)}^4$. Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in \left\{{\lambda }_1\pi ,\dots ,{\lambda }_r\pi \right\},$ where $0<$${\lambda }_1<\cdots <{\lambda }_r<1.$ Then the value of  ${\lambda }_1+\cdots +{\lambda }_r$ is_______