We multiply through by 1-cos(x) but if we do we
must rule out the case where the denominator
1-cos(x) would be 0, which would be when cos(x) = 1
which would be x=0°  



We change tan(x) to sin(x)/cos(x)



Distributing on the right gives:



We multiply through by cos(x) but if we do we
must rule out the case where the denominator
cos(x) would be 0, which would be when 
x = 90° or 270°  



We get 0 on the right:



Factor out sin(x)

 

Setting the first factor = 0,



x = 0° or 180° but we have ruled out x=0°,
so the only answer from setting the 
first factor = 0 is 180°

Setting the second factor = 0







Use calculator to get QI answer and
subtract it from 360° to get QIV answer. 
x = 36.86989765° and 323.1301024°

Solutions: 180°, 36.86989765°, 323.1301024°

Edwin