$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ =$$
$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ $$ =$$0+\frac{\sqrt{\ 3}}{2}-1+\frac{2}{\sqrt{\ 3}}+0\ =\ \frac{\left(7-2\sqrt{\ 3}\right)}{2\sqrt{\ 3}}=\frac{\left(7\sqrt{\ 3}-6\right)}{6}$$
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