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Show that cos^2(π/4) – cos^4(π/6) + sin^4(π/6) + sin^4(π/3) = 9/16

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Show that cos2(π/4) – cos4(π/6) + sin4(π/6) + sin4(π/3) = 9/16

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LHS: (1/√2)2  (√3/2)4 + (1/2)4 + (√3/2)4

= 1/2 - 9/16 + 1/16 + 9/16 = 9/16 = RHS

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