Given:
sin(theta) = cos(theta)

To Find:
The value of 2tan^2(theta) * sin^2(theta) - 1

Solution:

Step 1: Use the trigonometric identity: sin^2(theta) + cos^2(theta) = 1

Step 2: Rewrite the given equation using the above identity:
sin^2(theta) = 1 - cos^2(theta)

Step 3: Substitute sin^2(theta) in the expression to be evaluated:
2tan^2(theta) * (1 - cos^2(theta)) - 1

Step 4: Use the trigonometric identity: tan^2(theta) = 1 - cos^2(theta)

Step 5: Substitute tan^2(theta) in the expression:
2(1 - cos^2(theta)) * (1 - cos^2(theta)) - 1

Step 6: Simplify the expression:
2(1 - 2cos^2(theta) + cos^4(theta)) - 1

Step 7: Expand and simplify the expression:
2 - 4cos^2(theta) + 2cos^4(theta) - 1

Step 8: Combine like terms:
2cos^4(theta) - 4cos^2(theta) + 1

Step 9: Factor the expression:
(2cos^2(theta) - 1)^2

Step 10: Use the trigonometric identity: cos^2(theta) = 1 - sin^2(theta)

Step 11: Substitute cos^2(theta) in the expression:
(2(1 - sin^2(theta)) - 1)^2

Step 12: Simplify the expression:
(2 - 2sin^2(theta) - 1)^2

Step 13: Combine like terms:
(1 - 2sin^2(theta))^2

Step 14: Use the trigonometric identity: sin^2(theta) + cos^2(theta) = 1

Step 15: Substitute sin^2(theta) in the expression:
(1 - 2(1 - cos^2(theta)))^2

Step 16: Simplify the expression:
(1 - 2 + 2cos^2(theta))^2

Step 17: Combine like terms:
(2cos^2(theta) - 1)^2

Conclusion:
Therefore, the value of 2tan^2(theta) * sin^2(theta) - 1 is equal to (2cos^2(theta) - 1)^2.