(a) Start with the equation \(3 \tan^2 x - 3 \sin^2 x - 4 = 0\).

Replace \(\tan^2 x\) with \(\frac{\sin^2 x}{\cos^2 x}\) and multiply by \(\cos^2 x\):

\(3 \frac{\sin^2 x}{\cos^2 x} - 3 \sin^2 x - 4 = 0\)

\(3 \sin^2 x - 3 \sin^2 x \cos^2 x - 4 \cos^2 x = 0\)

Replace \(\sin^2 x\) by \(1 - \cos^2 x\):

\(3(1 - \cos^2 x) - 3(1 - \cos^2 x) \cos^2 x - 4 \cos^2 x = 0\)

\(3 - 3 \cos^2 x - 3 \cos^2 x + 3 \cos^4 x - 4 \cos^2 x = 0\)

\(3 \cos^4 x - 10 \cos^2 x + 3 = 0\)

Thus, \(a = 3\), \(b = -10\), \(c = 3\).

(b) Factor the equation:

\((3 \cos^2 x - 1)(\cos^2 x - 3) = 0\)

Solving \(3 \cos^2 x - 1 = 0\):

\(\cos^2 x = \frac{1}{3}\)

\(\cos x = \pm \frac{1}{\sqrt{3}}\)

Solving for \(x\) gives:

\(x = 54.7^\circ, 125.3^\circ\)