keep getting slightly wrong answer for integration question

"Use the substitution x=secθ where 0<=θ<π/2 to evaluate

(integrand) √(x^2-1)/x^4 dx."

so after substitution:

⌠ 2

⎮ √(SEC(θ) - 1)

⎮ ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ dx *(it still should be dx right? not d*θ?)

⎮ 4

⌡ SEC(θ)

after using trig identities I get (sigma)(1-sin^2θ)sinθcosθdx

the I let u = sinθ and -du=cosθdx

so

⌠ 3

- ⌡ (u - u ) du

and that is -(u^2)/2+(u^4)/4 +C

I suspect this is where I mess things up.

and then I plug back in the value of u to get

-(sin^2θ)/2+(sin^4θ)/4+c

my CAS gives me SIN(θ)^2·(SIN(θ)^2 - 2)/4 but I don't think that's the same(Doh)