tan(x)√3-sec(x)-1=0.
Multiply through by cos(x):
sin(x)√3-1-cos(x)=0,
sin(x)√3=1+cos(x).
cos(x)=2cos2(x/2)-1; sin(x)=2sin(x/2)cos(x/2).
2sin(x/2)cos(x/2)√3=2cos2(x/2),
2cos(x/2)(sin(x/2)√3-cos(x/2))=0,
cos(x/2)=0, x/2=π/2, x=π; or sin(x/2)√3=cos(x/2), tan(x/2)=1/√3, x/2=π/6, x=π/3.
There are many solutions because of the cyclic nature of the trig functions.
tan(x/2)=1/√3, x/2=2πn+(π/6 or 7π/6), which is the same as πn+π/6, x=2πn+π/3;
cos(x/2)=0, x/2=(2n+1)π/2, x=(2n+1)π. n is an integer (positive or negative).
To convert from radians to degrees, replace π by 180°.
In degrees: x=60, 180, 420, 540, 780, etc.