Calculate the value of following.
(i) `sec^2 60^\circ - cot^2 30^\circ - \frac{2 tan 30^\circ \text{cosec}\quad60^\circ}{1 + tan^2 30^\circ}`.
(ii) `\frac{tan 60^\circ - tan 30^\circ}{1 + tan60^\circ tan 30^\circ} + cos 60^\circ cos 30^\circ + sin 60^\circ sin 30^\circ`.
(iii) `cot^2 30^\circ - 2 cos^2 60^\circ - 3/4 sec^2 45^\circ - 4 sin^2 30^\circ`.
(iv) `\frac{5 cos^2 \frac{\pi}{3} + 4 sec^2 \frac{\pi}{6} - tan^2 \frac{\pi}{4}}{sin^2 \frac{\pi}{6} + cos^2 \frac{\pi}{6}}`.