'Di'gonometry

Geometry Level 5

Given that \(\dfrac{{\sin}^4 \theta}{5} + \dfrac{{\cos}^4 \theta}{7} = \dfrac{1}{12}\), find the value of \(\dfrac{{\sin}^{2016} \theta}{5^{1007}} + \dfrac{{\cos}^{2016} \theta}{7^{1007}}\).

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