Thank you very much your interest and answers. I dont know about most of the commands you used. I have to admit that I work with a damned old Student version 2 of Maple ( I assume that your advanced commands dont work on it... ). I forgot most about the theory of equations od degree 3 but I think that now it is proved that the value isnt transcendental. Right ? Am I wrong in my opinion that for the degree less then 5 I should expect an expression with radicals ? I like the formula sol[1] very much. I took the 3rd root value and tried to calculate Re() of it. No result with my version of Maple. But : evalc() worked/gave a result. Alas no radical expression ! I was very surprised that I could see/conclude the equation cos(arccos(13/14)/3)=cos(arctan(3*sqrt(3)/13)/3) which I already got from other considerations.