Find the exact value of each expression. (Do not use a calculator.)
cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)

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Recognize that the expression matches the cosine addition formula: \(\cos A \cos B - \sin A \sin B = \cos(A + B)\).

Identify the angles in the expression: \(A = \frac{7\pi}{9}\) and \(B = \frac{2\pi}{9}\).

Apply the formula by substituting the values of \(A\) and \(B\): \(\cos\left(\frac{7\pi}{9}\right) \cos\left(\frac{2\pi}{9}\right) - \sin\left(\frac{7\pi}{9}\right) \sin\left(\frac{2\pi}{9}\right) = \cos\left(\frac{7\pi}{9} + \frac{2\pi}{9}\right)\).

Add the angles inside the cosine function: \(\frac{7\pi}{9} + \frac{2\pi}{9} = \frac{9\pi}{9} = \pi\).

Use the known exact value of \(\cos \pi\) to find the final exact value.

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