= Solution
Put $s=\sin^2\alpha$ and $t=\sin^2\beta$. Then $0<s<t<1/2$, and the ordered squared <Schmidt coefficients> of the source and target are $(1-s,s)$ and $(1-t,t)$.
<Nielsen's pure-state conversion theorem> states that a deterministic exact conversion between bipartite pure states by <LOCC> exists precisely when the source's vector of squared <Schmidt coefficients> is majorized by the target's vector, with zero padding if needed. In the convention $x\prec y$, <majorization> requires $\sum_{j=1}^k x_j^\downarrow\leq\sum_{j=1}^k y_j^\downarrow$ for every $k$, and equality of total sums. Here the first inequality would require $1-s\leq1-t$, but $s<t$ gives the reverse strict inequality. Thus \b[exact conversion with certainty is impossible].
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