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# Trigonometric Equations

Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.

In the domain \( [0, 2 \pi ] \), how many solutions are there to

\[ 6 \cos^2 \theta - 10 \cos \theta + 3 \sin^2 \theta = 0 ? \]

Which of the following are the solutions to the equation

\[ 6 \tan^2 \theta - 17 \tan \theta + 2 \sec^2 \theta = 0 ? \]

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