SOLUTION: find all real solutions of cot^(2)3θ=3

From   = 3 you have two cases.


    a)   = ,  and

    b)   = - .



Let's consider these cases separately.


a)   = .


    Then  = 30°  or   = 210°;


         but since the problem talks about  ,  you must consider 
         
         also the angles        30° + 360° = 390°  and  30° + 720° = 750°;

         as well as the angles  210°+ 360° = 570°  and  210°+ 720° = 930°.


    These 6 angles for  ,         30°, 390°, 750°, 210°, 570° and 930°,  
    give 6 different angles for :  10°, 130°, 250°,  70°, 190° and 310°.




b)  Similarly  for   = - .


    Then  = 150°   or   = 330°;


         but since the problem talks about  ,  you must consider 
         
         also the angles        150° + 360° = 510°  and  150° + 720° = 870°;

         as well as the angles  330° + 360° = 690°  and  330° + 720° =1050°.


    These 6 angles for         ,  150°, 510°, 870°, 330°, 690° and 1050°,  
    give 6 different angles for :   50°, 170°, 290°, 110°, 230° and 350°.



Finally, these  6 + 6 = 12 angles gives you the full 


ANSWER.   10°,  130°,  250°,  70°,  190° and 310°,

          50°,  170°,  290°,  110°,  230° and 350°.