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

Correct Answer: 0.5

Answer is 0.5.