'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 $a$ .