MathDB

While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of

x

for which the sine of

x

degrees is the same as the sine of

x

radians are

\frac{m\pi}{n-\pi}

and

\frac{p\pi}{q+\pi},

where

m,

n,

p

and

q

are positive integers. Find

m+n+p+q.

Problem Statement