In a ΔABC right triangle at B. If sinC = \(\frac{60}{61}\) and cosA = \(\frac{60}{61}\), then find the value of the expression \(\frac{\text {tan}A + \text {cot} (A+C)}{\text {cot}C + \text {sec} A\text {sin} C}\).

1
\(\frac{11}{61}\)
2
\(\frac{11}{60}\)
3
\(\frac{11}{71}\)
4
\(\frac{11}{21}\)

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