# '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 $$a$$.

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