Use the information given about the angle theta, 0<theta<2pi to find the exact value

sin theta= 4/5 0
the answer is -7/25

But what are the steps to figure this out?
thank you!

Use the formula: cos(2Θ) = 1 - 2sin²Θ.

From here it's just plug-n-chug:

cos(2Θ) = 1 - 2(4/5)² = 1 - 32/25 = -7/25.

I'm going to use "x" in place of theta.
so sin(x) = 4/5
cos(2x) (by use of double-angle identities) = 1-2sin²x
cos(2x) = 1-2((4/5)²)
cos(2x) = 1-2(16/25)
cos(2x) = (25/25) - (32/25)
cos(2x) = -7/25