The Poisson bracket is $\{Q,P\}=Q_qP_p-Q_pP_q=2m q^{2m-1}(\cos^2p+\sin^2p)=2m q^{2m-1}$. A canonical pair requires this to be 1 for all q in its domain. Thus $2m-1=0$ and $2m=1$, both giving m = 0.5.
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