Hi Forum

I have some ideas myself on this one, but I'd love to hear how you guys would proceed in this scenario.

Find the sum of all solutions in the interval $\displaystyle [0,2\pi)$ for the equation $\displaystyle sec(3x)=\sqrt2$

First, we can put this in the form $\displaystyle cos(3x)=\frac{1}{\sqrt2}$ for better viewing.

We know that $\displaystyle cos(x)=\frac{1}{\sqrt2}$ is $\displaystyle \frac{\pi}{4}$ and $\displaystyle \frac{7\pi}{4}$.

Then our period will equal $\displaystyle \frac{2\pi}{3}$, so the distance from one $\displaystyle \sqrt2$ to another is $\displaystyle \frac{\pi}{3}$

Since our $\displaystyle \sqrt2$ will appear 3 times faster because of the $\displaystyle 3x$, our first $\displaystyle \sqrt2$ is $\displaystyle \frac{\pi}{12}$

Now, can we just go summing it to $\displaystyle \frac{\pi}{3}$ until we get to $\displaystyle 2\pi$?

What do you guys think?

Thanks!