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\displaystyle[br]\begin{equation*} 1 - \frac{3\sin^2 \theta}{\cos^2 \theta} \equiv \frac{\cos^2 \theta - 3\sin^2 \theta}{\cos^2 \theta} \equiv \frac{\cos^3 \theta - 3\cos \theta \sin^2 \theta}{\cos^3 \theta} \equiv \frac{\Re \left(\cos \theta + i\sin \theta\right)^3}{\cos^3 \theta} \equiv \frac{\cos 3\theta}{\cos^3 \theta} \end{equation*}
\displaystyle[br]\begin{equation*} 1 - \frac{3\sin^2 \theta}{\cos^2 \theta} \equiv \frac{\cos^2 \theta - 3\sin^2 \theta}{\cos^2 \theta} \equiv \frac{\cos^3 \theta - 3\cos \theta \sin^2 \theta}{\cos^3 \theta} \equiv \frac{\Re \left(\cos \theta + i\sin \theta\right)^3}{\cos^3 \theta} \equiv \frac{\cos 3\theta}{\cos^3 \theta} \end{equation*}
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