Strategy in finding limits

Minli's teacher gave her a flow chart (below) and asked her to find $\displaystyle\lim_{x\to \Large{\frac{\pi}{4}}}h(x)$limit, start subscript, x, \to, start fraction, pi, divided by, 4, end fraction, end subscript, h, left parenthesis, x, right parenthesis for $h(x)=\dfrac{2\sin(x)}{1-\cos(2x)}$h, left parenthesis, x, right parenthesis, equals, start fraction, 2, sine, left parenthesis, x, right parenthesis, divided by, 1, minus, cosine, left parenthesis, 2, x, right parenthesis, end fraction.