Solve `tan theta tan 4theta=1` for `0 lt theta lt pi`.

Answer

`theta=pi/10, (3 pi)/10, (5 pi)/10, (7 pi)/10, (9 pi)/10`

Explanation

The given equation can be written as
`cos 4 theta cos theta - sin 4 theta sin theta = 0`
`rArr cos 5 theta = 0`
`rArr 5 theta = (n + (1)/(2)) pi, n in Z`
`rArr theta = ((2n +1))/(10) pi, 0 lt theta lt pi, n in Z`
`= (pi)/(10), (3pi)/(10), (5pi)/(10), (7pi)/(10), (9pi)/(10)`
Thus, there are only five solutions in the given range