Help with finding the curvature URGENT

Definition of curvature: K = I r'(t) x r''(t) I / I r'(t) I³

r(t) = < -2sint, -2sint, -cost >
r'(t) = < -2cost, -2cost, sint >
r''(t) = < 2sint, .2sint, cost >

r'(t) x r''(t) =

I.....i..........j..........k I
I-2cost .-2cost..sintI
I2sint....2sint..-cost.I ...

= i(2cos²t - 2sin²t) - j(2cos²t - 2sin²t) + k(-4sintcost + 4sintcost)
r'(t) x r''(t) = i(2cos²t - 2sin²t) + j(2sin²t-2cos²t) + k*0 =
< -2sin²t + 2cos²t, 2sin²t - 2cos²t, 0 >

Ir'(t) x r''(t)I = √(4+4+0) = √8
Ir'(t)I = √(4cos²t + 4cos²t + sin²t) = √(sin²t+cos²t+7cos²t)
Ir'(t)I = √(1+7cos²t)
Ir'(t)I³ = ((1+7cos²t)^(3/2) , now we plug in the above in the def. of K:

K = I r'(t) x r''(t) I / I r'(t) I³

K = √8 / (1+7cos²t)^(3/2)
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