Find a trigonometric equation describing a given solution set

Write a trigonometric equation whose solution is the set given: $\space \bigg\{𝑥|𝑥 =\dfrac{\pi }{8}+\dfrac{\pi }{2𝑘} \space \lor \space 𝑥 =\dfrac{−\pi }{8}+\dfrac{\pi }{2𝑘},𝑘 ∈ 𝒁 \bigg\}$

From what is provided in the equation, 𝜋/2𝑘 is the period and it is possibly tangent. I am having trouble figuring out where to go next.

I have tried:

• graphing it on desmos to see if fiddling with it will magically show the equation.

• graphed it on a unit circle and I have found that it is possibly a tangent equation based on the +/- (𝜋/8). It is in the first and fourth quadrant, therefore its tangent.

• tried solving with the half-angle formula for tangent, but I get stuck figuring out where to input the what in the equation. I also don't know how to get cosine.

you have $$x=\pm\frac{\pi}{8}+\frac{\pi}{2k}$$ This can be rearranged as $$\frac{\pi^2}{x\mp\frac{\pi}{8}}=2k\pi$$ So one possible trig equation could be $$\sin\left(\frac{\pi^2}{x\mp\frac{\pi}{8}}\right)=0$$