I want to construct a periodic function that is build using sines or cosines that has the properties f(2n) = 1 and f(2n+1) = 2. (n is integer)

Now, I researched and found this Wikipedia article: Trignometric Interpolation.

But it doesn’t work as expected. I use the t_k formula from the article

to compute t0 and t1 but the sum

evaluates to

which does not satisfy my properties as listed above. Sample plot:

What am I doing wrong here?