Question

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

Answer 1

Answer is 0.5.