∵f(x)＝2sin2x−23sinxsin(x−π2)=2sin2x+23sinxcosx=1−cos2x+3sin2x=1+2sin(2x−π6)∵0＜x＜2π3∴−π6＜2x−π6＜7π6∴−12＜sin(2x−π6)≤1  即0＜f（x）≤3∵|f（x）-m|＜2 即m-2＜f（x）＜2+m在区...