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 $\theta \in \{\lambda_{1}\pi, \ldots, \lambda_{r}\pi\}$, where $0 < \lambda_{1} < \cdots < \lambda_{r} < 1$. Then the value of $\lambda_{1} + \cdots + \lambda_{r}$ is $\_\_\_\_$