**Solution:**

To find the value of the expression 2tan^2(sin^2) - 1, we first need to determine the value of sin and cos. Let's assume that sin(x) = cos(x) = k.

**Finding the Value of sin(x) and cos(x):**

Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can substitute k for both sin(x) and cos(x) to get:

k^2 + k^2 = 1
2k^2 = 1
k^2 = 1/2
k = ±√(1/2)

Since sin(x) and cos(x) can only take values between -1 and 1, we can conclude that k = ±1/√2.

Now, let's substitute the value of k back into the expression 2tan^2(sin^2) - 1.

**Calculating the Expression:**

Step 1: Substitute sin(x) and cos(x) with k in the expression.
2tan^2(sin^2) - 1 = 2tan^2(k^2) - 1

Step 2: Use the trigonometric identity tan^2(x) = sec^2(x) - 1.
2(sec^2(k^2) - 1) - 1

Step 3: Substitute sec^2(x) with 1 + tan^2(x).
2((1 + tan^2(k^2)) - 1) - 1

Step 4: Simplify the expression.
2(1 + tan^2(k^2) - 1) - 1
2tan^2(k^2) - 1

Step 5: Substitute the value of k.
2tan^2((1/√2)^2) - 1
2tan^2(1/2) - 1

Step 6: Use the trigonometric identity tan^2(x) = (1 - cos(2x))/ (1 + cos(2x)).
2((1 - cos(2(1/2)))/ (1 + cos(2(1/2)))) - 1
2((1 - cos(1))/ (1 + cos(1))) - 1

Step 7: Substitute the value of cos(1).
2((1 - cos(1))/ (1 + cos(1))) - 1

At this point, we are unable to simplify the expression further without knowing the exact value of cos(1). Therefore, the expression 2tan^2(sin^2) - 1 remains as it is.

Please note that the value of cos(1) is an irrational number and cannot be expressed exactly.