Trig Equations!

Using what you know about algebra (factoring, the quadratic formula, etc., etc.), and what you know about trigonometry (the unit circle, special right triangles, Pythagorean and other identities, etc.), solve the following equations for \(\theta\) (or whatever other obvious variable). That is, find all values of \(\theta\) that make the equation true. (Alllllll the values. And note that you might not be able to solve each equation exactly and might have to write some of your answers using an inverse trigonometric function!)

\(\sin(\theta) = 1/2\)
\(\cos(\theta) = 1/\sqrt{2}\)
\(\displaystyle\tan(\theta) = \frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)
\(\cos^2(\theta) = 3/4\)
\(\cos^2(\theta) = 1/2\)
\(\cos^2(\theta) = 0\)
\(\sin^2(\theta) = 1/4\)
\(\sin^2(\theta) = 1/2\)
\(\sin^2(\theta) = 1\)
\(\sin^2(\theta) - 1/4 = 0\)
\(\displaystyle \sin^2(\theta) - \frac{4 + 2\sqrt{3}}{8} = 0\)
\(\cos^2(\theta) - 1 = 0\)
\(\displaystyle \tan^2(\theta) - \frac{4 + 2\sqrt{3}}{4 - 2\sqrt{3}} = 0\)
\(\sin^2(\theta) - 5\sin(\theta) - \frac{1}{\sqrt{2}}\sin(\theta) + \frac{5}{\sqrt{2}} = 0\)
\(\sin^2(\theta) + \frac{3}{2}\sin{\theta} - 1 = 0\)
\(\sin(\theta)\cos(\theta) - \cos(\theta) - \frac{1}{\sqrt{2}}\sin(\theta) + \frac{1}{\sqrt{2}} = 0\)
\(2\cos^2(\theta) + \sin{\theta} + 1 = 0\)
\(\sin(3\theta) = \frac{\sqrt{3}}{2}\)
\(\sin(2\theta) = \sqrt{2}/2\)
\(\cos(5\theta) = (\sqrt{3} + 1)/(2\sqrt{2})\)
\(\tan(15\theta) = 0\)
\(\tan(\theta)\cos^2(\theta) = \tan(\theta)\)
\(3\sin^2(\theta) - 8\sin(\theta) = 3\)
\(5\cos^2(\theta) + 6\cos(\theta) = 0\)
\(2\tan^2(\theta) + 5\tan(\theta) + 3 = 0\)
\(3\sin^2(\theta) + 2\sin(\theta) = 5\)
\(\displaystyle \frac{\cos(\theta)}{\tan(\theta)} = \cos(\theta)\)
\(\tan(\theta)\cos(\theta) = \cos(\theta)\)
\(\displaystyle \cos(\theta)\cdot\frac{1}{\sin(\theta)} = 2\cos(\theta)\)
\(\displaystyle \tan(\theta)\cdot \frac{1}{\cos(\theta)} + 3\tan(\theta) = 0\)
\(4\sin(\theta)\tan(\theta) - 3\tan(\theta) + 20\sin(\theta) - 15 = 0\)
\(25\sin(\theta)\cos(\theta) - 5\sin(\theta) + 20\cos(\theta) = 4\)
\(\sin^2(\theta) + 2\sin(\theta) - 2 = 0\)
\(\cos^2(\theta) + 5\cos(\theta) = 1\)
\(\tan^2(\theta) + 1 = 3\tan(\theta)\)
\(4\cos^2(q) - 2\cos(q) = 1\)
\(2\tan^2(\theta) - 1 = 3\tan(\theta)\)
\(6\sin^2(\theta) + 4\sin(\theta) = 1\)
\(\displaystyle \frac{1}{\cos^2(\theta)} - 2\tan^2(\theta) = 0\)
\(9 - 12\sin(\theta) = 4\cos^2(\theta)\)
\(\displaystyle \frac{1}{\cos^2(\theta)} + \tan(\theta) = 3\)
\(\cos^2(\theta) - \sin^2(\theta) + \sin(\theta) = 0\)
\(2\tan^2(\theta) + \tan(\theta) = 5 - \frac{1}{\cos^2(\theta)}\)
\(\cos(\theta) = \sin(\theta)\)
\(\cos^2(\theta) = \sin^2(\theta)\)
\(\sin(\theta)\cos(\theta) - \frac{1}{\sqrt{2}}\cos(\theta) + \frac{\sqrt{3}}{2}\sin(\theta) - \frac{\sqrt{3}}{2\sqrt{2}} = 0\)
\(\tan(\theta)\sin(\theta) - \tan(\theta) + \sin(\theta) - 1 = 0\)
\(\cos^2(\theta) - \cos(\theta) - \frac{1}{\sqrt{2}}\cos(\theta) + \frac{1}{\sqrt{2}} = 0\)
\(\tan(\theta)\sin(\theta)\cos(4\theta) - \frac{\sqrt3}{2}\cos(4\theta)\tan(\theta) + \frac{1}{2}\frac{\sin^2(\theta)}{\cos(\theta)} - \frac{\sqrt3}{4}\tan(\theta) = 0\)
\(\ln\left(\cos \theta \right) - \frac12\ln(2) = 0\)
\(\ln\left(\sin x\right) + \frac12\ln(3) = 0\)
\(5e^{\sin t} - 5 = 0\)
\(\displaystyle \frac{6^{3+\tan x}}{1296} = 1\)
\(\ln(\cos \theta) = 0\)
\(\displaystyle \frac{\,\, e^{\sin x}\,\,}{\sqrt[\sqrt{2}]{e}} = 1\)
\(\displaystyle -\frac{1}{8} \, {\left(\pi - 2 \, \sin\left(5 \, \theta\right)\right)} {\left(\sqrt{2} {\left(\sqrt{3} + 1\right)} + 4 \, \cos\left(\theta\right)\right)} \cos\left(3 \, \theta\right) = 0\)