Let the minimum period of function f (x) = (sinwx + coswx) ^ + 2cos ^ Wx (W > 0) be 2 / 3, and find the value of W

Let the minimum period of function f (x) = (sinwx + coswx) ^ + 2cos ^ Wx (W > 0) be 2 / 3, and find the value of W

f(x)=(sinwx+coswx)²+2cos²wx
=1+2sinwxcoswx+cos2wx+1
=sin2wx+cos2wx+2
=√2sin(2wx+π/4)+2
Because 2 π / 2W = 2 π / 3, w = 3 / 2