\sin^2 120°\cosec 270° – \cos^2 315°\sec 180° – \tan^2 225°\cot 315° =

=\dfrac{\sin^2 120°}{\sin 270°} - \dfrac{\cos^2 315°}{\cos 180°} - \dfrac{\tan^2 225°}{\tan 315°}

=\dfrac{\sin^2 60°}{-\sin 90°} - \dfrac{\cos^2 45°}{-1} - \dfrac{\tan^2 45°}{-\tan 45°}

= - \dfrac{3}{4}+\dfrac{2}{4} +1

=\dfrac{3}{4}