List of top Mathematical Ability Questions on Trigonometry

If $\theta = 30^\circ$, then the value of \[ \frac{\sin^2\theta - \cos 2\theta}{\sin 2\theta + \cos^2\theta} \] is:

If $\sin\theta = \frac{3}{5}$ and $\theta<90^\circ$, then \[ \frac{\tan\theta - 2\cos\theta}{3\sin\theta + \sec\theta} = ? \]}