If `2sin^(2)theta=3costheta`, where `0lethetale2pi`, then find the value of `theta`.

Explanation

Given that, `" "2sin^(2)theta=3costheta`
`rArr" "2-2cos^(2)theta=3costheta`
`rArr" "2cos^(2)theta+3costheta-2 =0`
`rArr" "2cos^(2) theta+4costheta-costheta- 2=0`
`rArr" "2costheta(costheta+2)-1(costheta+2)=0`
`rArr" "(cos theta+2)(2costheta-1)=0`
`rArr" "costheta=-2 ` not possible `" "[because -1lecosthetale1]`
`" "2costheta=1`
`rArr" "cos theta=(1)/(2)`
`rArr" "costheta =cos""(pi)/(3)`
`therefore" "theta=(pi)/(3)`
Also, `" "costheta=cos(2pi-(pi)/(3) )`
`rArr" "costheta=cos""(5pi)/(6)`
`therefore" "theta=(5pi)/(6)`
So, the values of `theta` are `(pi)/(3) and (5pi)/(6)`.