This exercise provides another example of periodization: Apply the Poisson summation formula to the function in Exercise 15 (sin 7a) whenever a is real, but not equal to an integer. (b) Prove as a consequence that tan(a) is real but not equal to an integer. Hint: First prove it when 0 < a < 1. To do this, integrate the formula in (b). What is the precise meaning of the series on the left-hand side of (15)? Evaluate it at 1/2.