Let $\stackrel{\wedge }{a}$ and $\stackrel{\wedge }{b}$ be two unit vectors such that $|\stackrel{\wedge }{a}+\widehat{b}+2(\stackrel{\wedge }{a}\times \widehat{b})|=2,$ if $\theta \in (0,\pi )$ is the angle between $\stackrel{\wedge }{a} and\widehat{b}\text{.}$ Then $\theta =$   

${|\stackrel{\wedge }{a}+\widehat{b}+2(\stackrel{\wedge }{a}\times \widehat{b})|}^2=4$

${\left|\stackrel{\wedge }{a}\right|}^2+{\left|\widehat{b}\right|}^2+4{|\stackrel{\wedge }{a}\times \widehat{b}|}^2+2\stackrel{\wedge }{a}.\widehat{b}+4\widehat{b}(\stackrel{\wedge }{a}\times \widehat{b})+4\stackrel{\wedge }{a}(\stackrel{\wedge }{a}\times \widehat{b})=4$

$1+1+4{\sin }^2\theta +2\cos \theta =4$

$4{\sin }^2\theta +2\cos \theta =2$

$2{\sin }^2\theta +\cos \theta =1$

$2-2{\cos }^2\theta +\cos \theta =1$

$2{\cos }^2\theta -\cos \theta -1=0$

$2{\cos }^2\theta -2\cos \theta +\cos \theta -1=0$

$\cos \theta =1,-1/2$

$\theta =2\pi /3$