trigonometry - $sin 2x - tan 2x = -sin 2xtan 2x$ trigonometric identity proof

I need to prove

$$\sin 2x - \tan 2x = -\sin 2x\tan 2x$$

I tried simplifying
$$
\sin 2x = 2\sin x\cos x;\quad \tan 2x = \frac{2\tan x}{1-\tan^2x}.
$$

But it's so long and complicated that I feel I must've made a colossal mistake somewhere, or I am not using the correct equivalence. Or maybe I made a huge oversight from the beginning, and I don't need to simplify them in the first place.

Either way, i am stuck. Please help. Thanks.