Solve the equation
`tantheta-cottheta="cosec"theta`

Explanation

`tantheta-cottheta="cosec"theta`
`rArr (sintheta)/(costheta)-(costheta)/(sintheta)=1/(sintheta)`
`rArr (sin^(2)theta-cos^(2)theta)/(costhetasintheta)=1/(sintheta)`
`rArr sin^(2)theta-cos^(2)theta=costheta`
`rArr 1-cos^(2)theta-cos^(2)theta=costheta`
`rArr 2cos^(2)theta+costheta-1=0`
`rArr 2cos^(2)theta+2costheta-costheta-costheta-1=0`
`rArr 2costheta(costheta+1)-1(costheta+1)=0`
`rArr (costheta+1)(2costheta-1)=0`
`rArr costheta+1=0`or `2costheta-1=0`
Now `costheta+1=0`
`rArr costheta-1=-cos0=cospi`
andd `2costheta-1=0`
`rArr costheta=1/2=cospi/3`
`rArr theta=2npi+-pi/3`. Ans.