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{(\cos a - \cos b)}^{2} + {(\sin a - \sin b)}^{2} {[- 2 \sin (\frac{a + b}{2}) \sin (\frac{a - b}{2})]}^{2} + {[2 \cos (\frac{a + b}{2}) \sin (\frac{a - b}{2})]}^{2} = 4 \sin^{2} (\frac{a + b}{2}) \sin^{2} (\frac{a - b}{2}) + 4 \cos^{2} (\frac{a + b}{2}) \sin^{2} (\frac{a - b}{2}) = 4 \sin^{2} (\frac{a - b}{2}) [\sin^{2} (\frac{a + b}{2}) + \cos^{2} (\frac{a + b}{2})] = 4 \sin^{2} (\frac{a - b}{2}) [1] = 4 \sin^{2} (\frac{a - b}{2})

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