VMO 1971 Problem 1

Consider positive integers $m <n,p < q$ such that $(m, n) = 1, (p, q) = 1$ and satisfy the condition that if $\frac{m}{n}= tan\alpha$ and $\frac{p}{q} = tan\beta$ , then $\alpha + \beta = 45^o$ . i) Given $m, n$ , find $p, q$ . ii) Given $n, q$ , find $m, p$ . ii) Given $m, q$ , find $n, p$ .