Let the function : (0,𝜋)→ℝ be defined by
$ (\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \theta)^4 $
Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in\left\{\lambda_1 \pi, \ldots,
\lambda_{\mathrm{r}} \pi\right\}$, where $0<\lambda_1<\cdots<\lambda_r<1$. Then the value of $\lambda_1+\cdots+\lambda_r$ is $\_\_\_\_$