tan(2x-2/3π)=1
由2x-2/3π=π/4+kπ
2x=11/12 π+kπ
x=11/24 π+kπ/2
因为x∈[-π,2π]
即-π≤11/24 π+kπ/2≤2π
解得-35/12≤k≤37/12
故k=-2 -1 0 1 2 3
那么x=-13π/24 ,-π/24,11π/24,23π/24,35π/24,47π/24
祝学习快乐!