On completing three cyclic transversals to a latin square

Let $P$ be a partial latin square of prime order $p>7$ consisting of three cyclically generated transversals. Specifically, let $P$ be a partial latin square of the form: [ P={(i,c+i,s+i),(i,c+i,s+i),(i,c+i,s+i)mid 0 leq i< p} ] for some distinct $c,c,c$ and some distinct $s,s,s$. In this paper we show that any such $P$ completes to a latin square which is diagonally cyclic.