Why not expand it then?
(1 +sinX)(tanX -cotX) +2cosX = 0
tanX -cotX +sinXtanX -sinXcotX +2cosX = 0
tanX -cotX +sinX[sinX/cosX] -sinX[cosX/sinX] +2cosX = 0
tanX -cotX +[sin^2(X)/cosX] -cosX +2cosX = 0
tanX -cotX +[(1 -cos^2(X)) /cosX] +cosX = 0
tanX -cotX +[1/cosX -cosX] +cosX = 0
tanX -cotX +1/cosX = 0
sinX/cosX -cosX/sinX +1/cosX = 0
Clear the fractions, multiply both sides by sinXcosX,
sin^2(X) -cos^2(X) +sinX = 0
sin^2(X) -[1 -sin^2(X)] +sinX = 0
2sin^2(X) +sinX -1 = 0
(2sinX -1)(sinX +1) = 0
2sinX -1 = 0
sinX = 1/2
X = 30deg, 150deg
sinX +1 = 0
sinX = -1
X = 270 deg
The 30 and 150 degrees check with the original equation, but the 270 degress did not.
Therefore, in the interval 0 <= X <= 360deg,
X = 30 deg or 150 deg -------------------------answer.