A line makes angles 60$^\circ$, 45$^\circ$, $\theta$ with positive X, Y, Z-axes respectively. If $\theta$ is an acute angle, then $\tan\theta =$
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The fundamental identity for the direction cosines ($l, m, n$) of a line is $l^2+m^2+n^2=1$. This is equivalent to $\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1$, where $\alpha, \beta, \gamma$ are the angles the line makes with the coordinate axes.