Let the function $f:(0, \pi) \rightarrow R$ 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

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Let the function $f:(0, \pi) \rightarrow R$ 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 $0<\lambda_1<\ldots . .<\lambda_r<1$. Then the value of $\lambda_1+\ldots .+\lambda_{ r }$ is

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Let the function \(f:(0, \pi) \rightarrow R\) be defined by \(f(\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \t…

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