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Given that sin4θ5+cos4θ7=112\dfrac{{\sin}^4 \theta}{5} + \dfrac{{\cos}^4 \theta}{7} = \dfrac{1}{12}5sin4θ+7cos4θ=121, find the value of sin2016θ51007+cos2016θ71007\dfrac{{\sin}^{2016} \theta}{5^{1007}} + \dfrac{{\cos}^{2016} \theta}{7^{1007}}51007sin2016θ+71007cos2016θ.
The answer can be expressed as 12a{12}^{a}12a where aaa is a real number. Submit the value of aaa.
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