If the determinant cos⁡2x    sin2⁡x    cos⁡4xsin2⁡x    cos⁡2x    cos2⁡xcos⁡4x    cos2⁡x    cos⁡2x is expanded in powers of sin x, then the constant term in that expression is

f(x)=1−2sin2⁡xsin2⁡x1−8sin2⁡x1−sin2⁡xsin2⁡x1−2sin2⁡x1−sin2⁡x1−8sin2⁡x1−sin2⁡x1−sin2⁡x1−2sin2⁡xThe required constant term isf(0)=1    0    10    1    11    1    1=1    0    00    1    11    1    0=1(0−1)=−1