Let a, b, c ∈ R be such that a^2+ b^2+ c^2=1. If a cos θ= b cos (θ+(2 π)/3)= c cos (θ+(4 π)/3), where θ=(π)/9, then the angle between the vectors a i…

Let $\displaystyle \mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{R}$ be such that $\displaystyle \mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2=1$. If $\displaystyle \mathrm{a} \cos \theta=\mathrm{b} \cos \left(\theta+\frac{2 \pi}{3}\right)=\mathrm{c} \cos \left(\theta+\frac{4 \pi}{3}\right)$, where $\displaystyle \theta=\frac{\pi}{9}$, then the angle between the vectors $\displaystyle \mathrm{a} \hat{i}+\mathrm{b} \hat{j}+\mathrm{c} \hat{k}$ and $\displaystyle \mathrm{b} \hat{i}+\mathrm{c} \hat{j}+\mathrm{a} \hat{k}$ is :