**Solution:**

To find the value of theta such that A*A^(T) = I, we need to calculate the transpose of matrix A and then multiply it with A. Let's break down the steps:

**Step 1: Finding the transpose of matrix A**

The transpose of a matrix is obtained by interchanging its rows with columns. In this case, we have:

A = \[ cos(theta), -sin(theta) \]
\[ sin(theta), cos(theta) \]

Taking the transpose of matrix A, we get:

A^(T) = \[ cos(theta), sin(theta) \]
\[ -sin(theta), cos(theta) \]

**Step 2: Multiplying A with A^(T)**

Now, we will multiply matrix A with its transpose, A^(T):

A * A^(T) = \[ cos(theta)*cos(theta) - sin(theta)*(-sin(theta)), cos(theta)*sin(theta) - sin(theta)*cos(theta) \]
\[ sin(theta)*cos(theta) + cos(theta)*(-sin(theta)), sin(theta)*sin(theta) + cos(theta)*cos(theta) \]

Simplifying the above expression:

A * A^(T) = \[ cos^2(theta) + sin^2(theta), 0 \]
\[ 0, cos^2(theta) + sin^2(theta) \]

The resulting matrix is a diagonal matrix with 1's on the diagonal and 0's elsewhere, which is the identity matrix I.

**Step 3: Equating A * A^(T) with I**

Since A * A^(T) = I, we can equate the corresponding elements of both matrices:

\[ cos^2(theta) + sin^2(theta) = 1 \]
\[ cos^2(theta) + sin^2(theta) = 1 \]

Both equations are true for all values of theta. The value of theta can be any real number.

Therefore, the value of theta is not determined by the equation A * A^(T) = I. It can take any value in the real number system.