If `vec x and vecy` are unit vectors and `|vecz| = 2/sqrt7` such that `vecz + vecz xx vecx = vecy` then find the angle `theta` between `vecx and vecz`

Explanation

`vecz+vecz xx vecx = vecy or |vecz + veczxxvecx|^(2)= |vecy|^(2)`
or `|vecz|^(2)+ |vecz|^(2)|vecx|^(2)sin^(2) theta =1`
(because `vecz. (veczxx vecx) =0`)
`or |vecz|^(2) (1 + sin theta ) =1`
`or |vecz|^(2) = 1/(sqrt(1+sin^(2) theta))= 2/sqrt7`
`or sin theta = sqrt3//2`
`Rightarrow theta = pi//3 = 60^(@)`