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$\sin^{2} θ + \sin^{2} (60^{o} + θ) + \sin^{2} (60^{o} - θ) = ..................$

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Detailed Solution

$\begin{array}{l} G . E . = s i n^{2} θ + \sin^{2} (60^{o} + θ) + 1 - \cos^{2} (60^{o} - θ) = 1 + \frac{1 - \cos 2 θ}{2} - \cos 120^{o} \cos 2 θ \\ = 1 + \frac{1}{2} - \frac{1}{2} \cos 2 θ + \frac{1}{2} \cos 2 θ = \frac{3}{2} . \end{array}$

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