sin((3/4)*x +π/9) ≥(√3)/2 ;
arcsin(√3)/2 ≤ (3/4)*x +π/9 ≤ π - arcsin√(3)/2 ;
π/3 ≤ (3/4)*x + π/9 ≤ π - π/3 ;
π/3 -π/9 ≤ (3/4)*x ≤ π - π/3 -π/9 ;
2π/9 ≤ (3/4)*x ≤ 5π/9 ;
4*(2π/9)/3 ≤ x ≤ 4*(5π/9)/3 ;
8π/27 ≤ x ≤ 20π/27 ;
ответ: x ∈ [ 8π/27 ; 20π/27 ] .