Show there exists an infinite number of angles between 0 and p/2 whose sine and cosine are both rational.

         The Problem Solving Competition uses problems submitted by professors and students from different campuses throughout the United States and abroad. Each month the competition sends out problems to participating institutions. 
         To submit your solutions to the current problems, give them to Cathie Trigueiro in 108 Deady. Your solutions should be clearly written and should show all of your work and contain some mathematics. A correct solution for each problem will qualify for a drawing. You don't have to solve all of the problems. Just submit the ones you can solve. The person with the winning draw will receive a ten dollar gift certificate to Pegasus Pizza. Of course, this competition is for undergrads only.

         In Oregon university's early days, the student body referred to themselves as "Webfooters". L.H. Gregory, sports editor of The Oregonian, was given credit for using "Webfoots" as the school's original nickname. The paper's headline writers, however, started referring to the athletic teams as "Ducks" and Oregon's first live mascot became known as "Puddles" in the early 1920s. The mascot survived until the early 1940s when complaints from the Humane Society discouraged bringing a live duck to the games (geez!). Puddles managed to survive until 1947 when Oregon's first A.D., Leo Harris, reached an agreement with Walt Disney to have Donald Duck become the university's official mascot. Following Disney's death in 1966, it became apparent that a formal contract did not exist to allow the school the rights to Donald's image. But in 1973, a written contract was signed between Oregon's athletic department and Walt Disney Productions, which allowed the continued use of the famous cartoon character. Eventually, in 1984, Donald Duck (during the year of his 50^th birthday) was named as an honorary alumnus of the university.

         Show your work in solving the equation using appropriate operations on equations, and/or substitution. Give an exact answer, not an approximation.