**In this post, I wish to find the value of some finite product. I begin by defining** **a function** **as follows and trying to find it’s roots
**

**Let** **, then we have**

**and similarly** **.** **So we have**

**The sine function vanishes at integer multiples of** **, so it follows that** ** where** ** for all integers** **, that is, for** **for all** **. Thus,** **for**

**where we recall that** **. Since** **is strictly increasing on the interval** **, it** **follows that**

**moreover, since tangent is an odd function, we have** **for each** **. In particular we have found** **distinct roots of** **, so as a consequence of the fundamental theorem of algebra, we can write**

**So we have ****, and**