'Di'gonometry

Geometry Level 5

Given that sin4θ5+cos4θ7=112\dfrac{{\sin}^4 \theta}{5} + \dfrac{{\cos}^4 \theta}{7} = \dfrac{1}{12}, find the value of sin2016θ51007+cos2016θ71007\dfrac{{\sin}^{2016} \theta}{5^{1007}} + \dfrac{{\cos}^{2016} \theta}{7^{1007}}.

The answer can be expressed as 12a{12}^{a} where aa is a real number. Submit the value of aa.

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