Calculate without the use of calculator \( \frac{\cos ^{2} 213^{\circ}}{\tan 135^{\circ}-\sin 147^{\circ} \cdot \sin 327^{\circ}} \)

Let's break down the expression step by step, shall we? First, we know that \(\tan 135^{\circ} = -1\), because \(\tan(180^{\circ} - 45^{\circ}) = -\tan 45^{\circ}\). Now for \(-\sin 147^{\circ} \cdot \sin 327^{\circ}\). We can find these values: - \(\sin 147^{\circ} = \sin(180^{\circ} - 33^{\circ}) = \sin 33^{\circ}\). - \(\sin 327^{\circ} = \sin(360^{\circ} - 33^{\circ}) = -\sin 33^{\circ}\). So, \(-\sin 147^{\circ} \cdot \sin 327^{\circ} = -\sin 33^{\circ} \cdot (-\sin 33^{\circ}) = \sin^2 33^{\circ}\). Putting these together, we have: \[ \tan 135^{\circ} - \sin 147^{\circ} \cdot \sin 327^{\circ} = -1 - \sin^2 33^{\circ}. \] Next, we calculate \(\cos^2 213^{\circ}\). \(\cos 213^{\circ} = \cos(180^{\circ} + 33^{\circ}) = -\cos 33^{\circ}\), thus \(\cos^2 213^{\circ} = \cos^2 33^{\circ}\). Now our original expression becomes: \[ \frac{\cos^2 33^{\circ}}{-1 - \sin^2 33^{\circ}}. \] Since \(\sin^2 33^{\circ} + \cos^2 33^{\circ} = 1\), we have: \[ -1 - \sin^2 33^{\circ} = -1 - (1 - \cos^2 33^{\circ}) = -\cos^2 33^{\circ}. \] Now we've arrived at: \[ \frac{\cos^2 33^{\circ}}{-\cos^2 33^{\circ}} = -1. \] So the final answer is: \[ \boxed{-1}. \]