Find the number of pairs (m, n) of positive integers with 1 \leq m<n \leq 30 such that there exists a real number x satisfying

\sin (m x)+\sin (n x)=2

Find the number of pairs (m, n) of positive integers with 1 \leq m<n \leq 30 such that there exists a real number x satisfying

\sin (m x)+\sin (n x)=2