Proof of trignometric identity Could you help me prove this? I've gotten stuck, need some help..

$$\sin^2\Theta + \tan^2\Theta = \sec^2\Theta - \cos^2\Theta$$

Here's what I've done so far:
Left Side:
$$\sin^2\Theta + \frac{\sin^2\Theta}{\cos^2\Theta}=\frac{\sin^2\Theta\cos^2\Theta+\sin^2\Theta}{\cos^2\Theta}$$
Right Side:
$$\frac{1}{\cos^2\Theta} - \cos^2\Theta = \frac{1-\cos^2\Theta\cos^2\Theta}{\cos^2\Theta}$$
Thanks in advance.
Note: I have tried simplifying it even further but I'm not getting the results, so I've left it at the points that I'm sure of.

Hint: $\sin^2\theta+\cos^2\theta=1.$
