Trigo is not such easy!!

Algebra Level 5

If given \[[2cosx] + [sinx]=-3\] Then the range of the function \[ f(x)=sinx+\sqrt{3}cosx\] can be written as \[[a,b]\] Where \[x\in[0,2π]\]

Find the value of \[a^{2}+b^{2}\]

\[Note: Here [a] represents G.I.F \]

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