The value of $\sec ^4 \theta\left(1-\sin ^4 \theta\right)-2 \tan ^2 \theta$ is:

1 

sec4 θ ( 1 - sin4 θ ) - 2 tan²θ 

\(\frac{1 }{cos4 θ}\)× ( 1 - sin² θ ) × ( 1 + sin² θ ) - 2 tan²θ

{ using , sin² θ  +  cos² θ = 1 }

= \(\frac{1 }{cos4 θ}\)× ( cos² θ ) × ( 1 + sin² θ ) - 2 tan²θ

= \(\frac{1 }{cos² θ}\) × ( 1 + sin² θ ) - 2\(\frac{sin² θ }{cos² θ}\)

= \(\frac{1 + sin² θ - 2 sin² θ }{cos² θ}\) 

= \(\frac{1 - sin² θ }{cos² θ}\)

= \(\frac{cos² θ }{cos² θ}\)

= 1