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Verified answer

3ctq²(3π/2 +x/3) -2tq(x/3) =1;
3tq²(x/3) -2tq(x/3) - 1 =0 ;
* * кв. уравнения относительно  tq(x/3),можно и пров. замену  t =tq(x/3) *
D/4 =1 -3(-1) =4 =2² .
tq(x/3) =(1± 2)/3.
[ tq(x/3) = -1/3 ;  tq(x/3)  =1. (совокупность) 
[ x/3 = -arctq(1/3)+π*n , x/3  =π/4 +π*n , n ∈ Z.
[ x = -3arctq(1/3)+3π*n , x  =3π/4 +3π*n , n ∈ Z.

ответ : -3arctq(1/3)+3π*n , x  =3π/4 +3π*n , n ∈ Z.