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If \( A, B \) and \( C \) are the angles of a triangle, prove that:
(i) \( \sin \left(\frac{A}{2}\right) \sin \left(\frac{B}{2}\right) \sin \left(\frac{C}{2}\right) \leq \frac{1}{8} \)
(ii) \( \cos \left(\frac{A}{2}\right) \cos \left(\frac{B}{2}\right) \cos \left(\frac{C}{2}\right) \leq \frac{3 \sqrt{3}}{8} \)
(iii) \( \cos A+\cos B+\cos C \leq \frac{3}{2} \).
(iv) \( \tan ^{2}\left(\frac{A}{2}\right)+\tan ^{2}\left(\frac{B}{2}\right)+\tan ^{2}\left(\frac{C}{2}\right) \geq 1 \).
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