Question: Conversion of trigonmetric expression to radicals

Hi,

with great interest and surprise I read the post
"Converting Half-Angle Trig Formulas to Radicals".
Isnt it possible to evaluate cos(arccos(13/14)/3) also
to an exact expression in radicals ?
I simply do not succeed with my humble knowledge of
the Maple commands/internal workings...
Would be great if someone finds a solution ( of an 
unsolvable problem ??? ).

[Edit: Excess white space deleted.---Carl Love]

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