JEE Math Practice Question

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