First, factor the quadratic equation:

\(8 \cos^2 \theta - 10 \cos \theta + 2 = 0\)

can be factored as \(2(4 \cos \theta - 1)(\cos \theta - 1) = 0\).

This gives two equations:

1. \(4 \cos \theta - 1 = 0\)

2. \(\cos \theta - 1 = 0\)

Solving the first equation:

\(4 \cos \theta = 1\)

\(\cos \theta = \frac{1}{4}\)

\(\theta = 75.5^\circ\) (using a calculator for inverse cosine)

Solving the second equation:

\(\cos \theta = 1\)

\(\theta = 0^\circ\)

Thus, the solutions are \(\theta = 0^\circ\) and \(\theta = 75.5^\circ\).