f(x) = sin2x - 2√3 sin²x + √3 +1
= sin2x - √3 (1 - cos2x) + √3 + 1
= sin2x + √3 cos2x + 1
= 2 sin(2x + π/3) + 1
最小正周期 T = 2π/2 = π
- π/2 + 2kπ < 2x+ π/3 < π/2 + 2kπ
解得增区间 ( - 5π/12 + kπ,π/12 + kπ)