2017 blocks each of mass \(m = \SI{20.17}{\kilogram}\) are connected by massless strings and the whole system is fixed to a rigid ceiling, as shown above.

A constant force \(F = mg\) acts on the \(2017^\text{th}\) block and displaces it. As a result, the entire system is disturbed and subsequently settles into a stationary equilibrium. In the equilibrium position, the string above block \(i\) subtends an acute angle of \( \theta_i\) with the vertical.

What is \(\theta_1\) (in degrees) to 3 decimal places? Take acceleration due to gravity as \(g=\SI[per-mode=symbol]{9.80}{\meter \per \second \squared}.\)

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