$\displaystyle sin \theta = \frac{36cos\theta -12}{128}$
$\displaystyle 36cos\theta - 128sin\theta = 12$
$\displaystyle
9cos\theta - 32sin\theta = 3$
$\displaystyle \frac{9}{\sqrt{9^2+32^2}}cos\theta - \frac{32}{\sqrt{9^2+32^2}}sin\theta = \frac{3}{\sqrt{9^2+32^2}}$
$\displaystyle sin\alpha cos\theta - cos\alpha sin\theta = \frac{3}{\sqrt{9^2+32^2}}$
$\displaystyle sin(\alpha - \theta) = \frac{3}{\sqrt{9^2+32^2}}$
$\displaystyle \theta = \alpha - sin^-1(\frac{3}{\sqrt{9^2+32^2}})$
where $\displaystyle \alpha = sin^-1(\frac{9}{\sqrt{9^2+32^2}})$