Test your understanding of solving trig equations and inverse trig functions.
1. Solve $2\\sin^2\\theta - \\sin\\theta - 1 = 0$ for $0 \\le \\theta < 2\\pi$. (3 marks)
2. Solve $\sin(2\\theta) = \\frac{\\sqrt{3}}{2}$ for $0 \\le \\theta < 2\\pi$. (3 marks)
3. Find the exact value of $\cos^{-1}(-\\frac{1}{2})$. (1 mark)
4. Sketch $y = \\tan^{-1}x$, showing asymptotes and key points. (3 marks)