Find the number of solution of the equation `(2sintheta-sin3theta)/(1+costheta)+(3costheta+cos3theta)/(1-sintheta)=4sqrt(2)cos(theta+(pi)/(4))`
in the interval `(-10pi,8pi].`

Explanation

`(3sintheta-(3sintheta-4sin^(3)theta))/(1+costheta)+(3costheta+(4cos^(3)theta-3costheta))/(1-sintheta)=4sqrt(2)cos(theta+(pi)/(4))`
`implies4sintheta(1-costheta)-4costheta(1+sintheta)=4sqrt(2)cos(theta+(pi)/(4))`
`implies4sqrt(2)sin(theta+(pi)/(4))=4sqrt(2)cos(theta+(pi)/(4))impliestan(theta+(pi)/(4))=1impliestheta+(pi)/(4)=npi+(pi)/(4),nin"I"`
But `1+costhetane0`
`:." "theta=2npiAAnin"I"`
Hence number of solutiohn are `9" i.e. "theta=-8pi,-6pi,-4pi,-2pi,0,2pi,4pi,6pi,8pi.`