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How do you solve this trigonometric equation?

Solve the equation for solutions in the interval $[0,2 \pi)$. $\left(\cot(x) -1 \right) \left( 2 \sin(x) + \sqrt{3} \right) = 0.$

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    The pro$f$anity in the user's display name has been removed. @I'm just some guy: Any future use of profanity will be cause for suspension.2012-05-06

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A product of two real valued quantities is zero if and only if one of the terms in the product is zero.

So, here, either $ \cot x-1=0 $ or $ 2\sin x +\sqrt 3=0. $ Equivalently either $\cot x=1$ or $\sin x =-\sqrt 3/2$. Can you find the solutions to these? Remember to only take solutions in $[0,2\pi)$.

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    Yep, I found the correct solution set as {pi/4, 5pi/4, 4pi/3, 5pi/3}. Thanks!2012-05-06