In deriving Eq$.12\mathrm{.}5,$ we assumed that when $$ is small, $sin=.$ In this case, the period is a constant that does not depend on the size of the oscillations. However, if $$ becomes large, the above approximation is no longer valid and the period becomes dependent on the amplitude:

$T=2\sqrt[\phantom{2}]{\frac{L}{g}}(1+\frac{1}{16}{}^2+\frac{11}{3072}{}^4+$dots$)$

Using the first two terms of this equation, calculate by what percent the period of the pendulum used in this experiment would change if it was dropped from $45$ instead of $10.$