Value of the expression \( \log _{1 / 2}\left(\sin 6^{\circ} \cdot \sin 42^{\circ} \cdot \sin 45...

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Value of the expression \( \log _{1 / 2}\left(\sin 6^{\circ} \cdot \sin 42^{\circ} \cdot \sin 45^{\circ}\right. \) \( \left.\sin 66^{\circ} \cdot \sin 78^{\circ}\right) \)
(a) Lies between 4 and 5
(b) Is rational which is not integral
(c) Is irrational which is a simple surd
(d) Is irrational which is a mixed surd
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